Найти производную y' = f'(x) = cos(x)/(Abs(cos(x))) (косинус от (х) делить на (Abs(косинус от (х)))) - функции. Найдём значение производной функции в точке. [Есть ответ!]
Производная функции/ От одной переменной/ y' = (cos(x)/(Abs(cos(x))))'

Производная cos(x)/(Abs(cos(x)))

Учитель очень удивится увидев твоё верное решение производной 😼

()'

– производная -го порядка в точке

Примеры

График:

от до

Кусочно-заданная:

{ кусочно-заданную функцию ввести здесь.

Решение

Вы ввели [src]
 cos(x) 
--------
|cos(x)|
$$\frac{\cos{\left (x \right )}}{\left|{\cos{\left (x \right )}}\right|}$$
Первая производная [src]
             //d                                  d                               \                          /  d                                  d                               \                       \       
             ||--(im(x))*cos(re(x))*sinh(im(x)) - --(re(x))*cosh(im(x))*sin(re(x))|*cos(re(x))*cosh(im(x)) - |- --(im(x))*cosh(im(x))*sin(re(x)) - --(re(x))*cos(re(x))*sinh(im(x))|*sin(re(x))*sinh(im(x))|*cos(x)
   sin(x)    \\dx                                 dx                              /                          \  dx                                 dx                              /                       /       
- -------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
  |cos(x)|                                                                                                         3                                                                                               
                                                                                                           |cos(x)|
$$- \frac{\cos{\left (x \right )}}{\left|{\cos{\left (x \right )}}\right|^{3}} \left(\left(- \sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} + \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}\right) \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} - \left(- \sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} - \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}\right) \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )}\right) - \frac{\sin{\left (x \right )}}{\left|{\cos{\left (x \right )}}\right|}$$
Упростить
Вторая производная [src]
          //           2                            2                                   2                                            2                                                                      \                          /           2                            2                                            2                            2                                                                             \                                                                                                                                                                                                                                                                                                                                                                                                                                                           \                                                                                                                                                                                                                                                                                                                                                                                                                          
          ||/d        \                            d                                   d                                  /d        \                             d         d                               |                          |/d        \                            d                                  /d        \                            d                                    d         d                               |                          /d                                  d                               \ d                                  /d                                  d                               \ d                                  /d                                  d                               \ d                                  /d                                  d                               \ d                               |                                                                                                                                                                                                                                                                                                                                                                                                                  2       
          |||--(im(x))| *sin(re(x))*sinh(im(x)) + ---(im(x))*cosh(im(x))*sin(re(x)) + ---(re(x))*cos(re(x))*sinh(im(x)) - |--(re(x))| *sin(re(x))*sinh(im(x)) + 2*--(im(x))*--(re(x))*cos(re(x))*cosh(im(x))|*sin(re(x))*sinh(im(x)) - ||--(re(x))| *cos(re(x))*cosh(im(x)) + ---(re(x))*cosh(im(x))*sin(re(x)) - |--(im(x))| *cos(re(x))*cosh(im(x)) - ---(im(x))*cos(re(x))*sinh(im(x)) + 2*--(im(x))*--(re(x))*sin(re(x))*sinh(im(x))|*cos(re(x))*cosh(im(x)) + |--(im(x))*cosh(im(x))*sin(re(x)) + --(re(x))*cos(re(x))*sinh(im(x))|*--(im(x))*cosh(im(x))*sin(re(x)) + |--(im(x))*cosh(im(x))*sin(re(x)) + --(re(x))*cos(re(x))*sinh(im(x))|*--(re(x))*cos(re(x))*sinh(im(x)) + |--(re(x))*cosh(im(x))*sin(re(x)) - --(im(x))*cos(re(x))*sinh(im(x))|*--(re(x))*cosh(im(x))*sin(re(x)) - |--(re(x))*cosh(im(x))*sin(re(x)) - --(im(x))*cos(re(x))*sinh(im(x))|*--(im(x))*cos(re(x))*sinh(im(x))|*cos(x)     //d                                  d                               \                          /d                                  d                               \                       \            //d                                  d                               \                          /d                                  d                               \                       \        
          ||\dx       /                             2                                   2                                 \dx       /                             dx        dx                              |                          |\dx       /                             2                                 \dx       /                             2                                   dx        dx                              |                          \dx                                 dx                              / dx                                 \dx                                 dx                              / dx                                 \dx                                 dx                              / dx                                 \dx                                 dx                              / dx                              |          2*||--(re(x))*cosh(im(x))*sin(re(x)) - --(im(x))*cos(re(x))*sinh(im(x))|*cos(re(x))*cosh(im(x)) - |--(im(x))*cosh(im(x))*sin(re(x)) + --(re(x))*cos(re(x))*sinh(im(x))|*sin(re(x))*sinh(im(x))|*sin(x)   3*||--(re(x))*cosh(im(x))*sin(re(x)) - --(im(x))*cos(re(x))*sinh(im(x))|*cos(re(x))*cosh(im(x)) - |--(im(x))*cosh(im(x))*sin(re(x)) + --(re(x))*cos(re(x))*sinh(im(x))|*sin(re(x))*sinh(im(x))| *cos(x)
          \\                                      dx                                  dx                                                                                                                    /                          \                                      dx                                                                        dx                                                                              /                                                                                                                                                                                                                                                                                                                                                                                                                                                           /            \\dx                                 dx                              /                          \dx                                 dx                              /                       /            \\dx                                 dx                              /                          \dx                                 dx                              /                       /        
-cos(x) - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                                                                                                                                                                                                              2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      2                                                                                                                                                                                                         4                                                                                               
                                                                                                                                                                                                                                                                                                                                                                                                                                                      |cos(x)|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               |cos(x)|                                                                                                                                                                                                  |cos(x)|                                                                                                
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            |cos(x)|
$$\frac{1}{\left|{\cos{\left (x \right )}}\right|} \left(\frac{3 \cos{\left (x \right )}}{\left|{\cos{\left (x \right )}}\right|^{4}} \left(\left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} - \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}\right) \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} - \left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} + \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}\right) \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )}\right)^{2} - \frac{2 \sin{\left (x \right )}}{\left|{\cos{\left (x \right )}}\right|^{2}} \left(\left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} - \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}\right) \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} - \left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} + \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}\right) \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )}\right) - \frac{\cos{\left (x \right )}}{\left|{\cos{\left (x \right )}}\right|^{2}} \left(\left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} - \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}\right) \sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} - \left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} - \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}\right) \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} + \left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} + \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}\right) \sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} + \left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} + \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}\right) \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} + \left(- \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}^{2} + \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}^{2} + \sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d^{2}}{d x^{2}} \Im{x} + \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d^{2}}{d x^{2}} \Re{x} + 2 \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} \frac{d}{d x} \Im{x}\right) \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} - \left(2 \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} \frac{d}{d x} \Im{x} + \sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d^{2}}{d x^{2}} \Re{x} - \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d^{2}}{d x^{2}} \Im{x} + \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}^{2} - \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}^{2}\right) \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )}\right) - \cos{\left (x \right )}\right)$$
Упростить
Третья производная [src]
  //           3                            3                                   3                                            3                                       2                                                  2                                              2                                                  2                                               2                                               2                              \                          /  3                                            3                                     3                            3                                               2                                              2                                                 2                                                  2                                               2                                               2                              \                                     2                                                                                                           2                                                                                                                                                                        2                                                                                                         2                                                                                                         2                                            2                                                                                                           2                                                                                                                                                                        2                                   /           2                            2                                            2                            2                                                                             \                                      /           2                            2                                   2                                            2                                                                      \                                      /           2                            2                                   2                                            2                                                                      \                                      /           2                            2                                            2                            2                                                                             \                                                                                                                                                                                                                                                                           \                                                                                                                                                                                                                                                                                                                                                                                                                               //           2                            2                                   2                                            2                                                                      \                          /           2                            2                                            2                            2                                                                             \                                                                                                                                                                                                                                                                                                                                                                                                                                                           \                                                                                                                                                                                                                                                                                                                                                                                                                     //           2                            2                                   2                                            2                                                                      \                          /           2                            2                                            2                            2                                                                             \                                                                                                                                                                                                                                                                                                                                                                                                                                                           \                
  ||/d        \                            d                                   d                                  /d        \                             /d        \  d                                    d          d                                    /d        \  d                                    d          d                                    d          d                                    d          d                               |                          | d                                  /d        \                           /d        \                            d                                    d          d                                    /d        \  d                                    /d        \  d                                    d          d                                    d          d                                    d          d                               |                          /d        \  /d                                  d                               \                          /d        \  /d                                  d                               \                          /d                                  d                               \  d                                  /d                                  d                               \  d                                  /d                                  d                               \  d                                  /d        \  /d                                  d                               \                          /d        \  /d                                  d                               \                          /d                                  d                               \  d                                    |/d        \                            d                                  /d        \                            d                                    d         d                               | d                                    |/d        \                            d                                   d                                  /d        \                             d         d                               | d                                    |/d        \                            d                                   d                                  /d        \                             d         d                               | d                                    |/d        \                            d                                  /d        \                            d                                    d         d                               | d                                    /d                                  d                               \ d         d                                    /d                                  d                               \ d         d                               |                                                                                                                                                                                                         2                                                                                                                                                                                                                     ||/d        \                            d                                   d                                  /d        \                             d         d                               |                          |/d        \                            d                                  /d        \                            d                                    d         d                               |                          /d                                  d                               \ d                                  /d                                  d                               \ d                                  /d                                  d                               \ d                                  /d                                  d                               \ d                               |                                                                                                                                                                                                          3            //d                                  d                               \                          /d                                  d                               \                       \ ||/d        \                            d                                   d                                  /d        \                             d         d                               |                          |/d        \                            d                                  /d        \                            d                                    d         d                               |                          /d                                  d                               \ d                                  /d                                  d                               \ d                                  /d                                  d                               \ d                                  /d                                  d                               \ d                               |                
  |||--(im(x))| *cosh(im(x))*sin(re(x)) + ---(im(x))*cosh(im(x))*sin(re(x)) + ---(re(x))*cos(re(x))*sinh(im(x)) - |--(re(x))| *cos(re(x))*sinh(im(x)) - 3*|--(re(x))| *--(im(x))*cosh(im(x))*sin(re(x)) - 3*--(re(x))*---(re(x))*sin(re(x))*sinh(im(x)) + 3*|--(im(x))| *--(re(x))*cos(re(x))*sinh(im(x)) + 3*--(im(x))*---(im(x))*sin(re(x))*sinh(im(x)) + 3*--(im(x))*---(re(x))*cos(re(x))*cosh(im(x)) + 3*--(re(x))*---(im(x))*cos(re(x))*cosh(im(x))|*sin(re(x))*sinh(im(x)) - |---(re(x))*cosh(im(x))*sin(re(x)) - |--(im(x))| *cos(re(x))*sinh(im(x)) - |--(re(x))| *cosh(im(x))*sin(re(x)) - ---(im(x))*cos(re(x))*sinh(im(x)) - 3*--(im(x))*---(im(x))*cos(re(x))*cosh(im(x)) + 3*|--(im(x))| *--(re(x))*cosh(im(x))*sin(re(x)) + 3*|--(re(x))| *--(im(x))*cos(re(x))*sinh(im(x)) + 3*--(im(x))*---(re(x))*sin(re(x))*sinh(im(x)) + 3*--(re(x))*---(im(x))*sin(re(x))*sinh(im(x)) + 3*--(re(x))*---(re(x))*cos(re(x))*cosh(im(x))|*cos(re(x))*cosh(im(x)) + |--(im(x))| *|--(im(x))*cosh(im(x))*sin(re(x)) + --(re(x))*cos(re(x))*sinh(im(x))|*sin(re(x))*sinh(im(x)) + |--(re(x))| *|--(re(x))*cosh(im(x))*sin(re(x)) - --(im(x))*cos(re(x))*sinh(im(x))|*cos(re(x))*cosh(im(x)) + |--(im(x))*cosh(im(x))*sin(re(x)) + --(re(x))*cos(re(x))*sinh(im(x))|*---(im(x))*cosh(im(x))*sin(re(x)) + |--(im(x))*cosh(im(x))*sin(re(x)) + --(re(x))*cos(re(x))*sinh(im(x))|*---(re(x))*cos(re(x))*sinh(im(x)) + |--(re(x))*cosh(im(x))*sin(re(x)) - --(im(x))*cos(re(x))*sinh(im(x))|*---(re(x))*cosh(im(x))*sin(re(x)) - |--(im(x))| *|--(re(x))*cosh(im(x))*sin(re(x)) - --(im(x))*cos(re(x))*sinh(im(x))|*cos(re(x))*cosh(im(x)) - |--(re(x))| *|--(im(x))*cosh(im(x))*sin(re(x)) + --(re(x))*cos(re(x))*sinh(im(x))|*sin(re(x))*sinh(im(x)) - |--(re(x))*cosh(im(x))*sin(re(x)) - --(im(x))*cos(re(x))*sinh(im(x))|*---(im(x))*cos(re(x))*sinh(im(x)) - 2*||--(re(x))| *cos(re(x))*cosh(im(x)) + ---(re(x))*cosh(im(x))*sin(re(x)) - |--(im(x))| *cos(re(x))*cosh(im(x)) - ---(im(x))*cos(re(x))*sinh(im(x)) + 2*--(im(x))*--(re(x))*sin(re(x))*sinh(im(x))|*--(im(x))*cos(re(x))*sinh(im(x)) + 2*||--(im(x))| *sin(re(x))*sinh(im(x)) + ---(im(x))*cosh(im(x))*sin(re(x)) + ---(re(x))*cos(re(x))*sinh(im(x)) - |--(re(x))| *sin(re(x))*sinh(im(x)) + 2*--(im(x))*--(re(x))*cos(re(x))*cosh(im(x))|*--(im(x))*cosh(im(x))*sin(re(x)) + 2*||--(im(x))| *sin(re(x))*sinh(im(x)) + ---(im(x))*cosh(im(x))*sin(re(x)) + ---(re(x))*cos(re(x))*sinh(im(x)) - |--(re(x))| *sin(re(x))*sinh(im(x)) + 2*--(im(x))*--(re(x))*cos(re(x))*cosh(im(x))|*--(re(x))*cos(re(x))*sinh(im(x)) + 2*||--(re(x))| *cos(re(x))*cosh(im(x)) + ---(re(x))*cosh(im(x))*sin(re(x)) - |--(im(x))| *cos(re(x))*cosh(im(x)) - ---(im(x))*cos(re(x))*sinh(im(x)) + 2*--(im(x))*--(re(x))*sin(re(x))*sinh(im(x))|*--(re(x))*cosh(im(x))*sin(re(x)) + 2*|--(im(x))*cosh(im(x))*sin(re(x)) + --(re(x))*cos(re(x))*sinh(im(x))|*--(im(x))*--(re(x))*cos(re(x))*cosh(im(x)) + 2*|--(re(x))*cosh(im(x))*sin(re(x)) - --(im(x))*cos(re(x))*sinh(im(x))|*--(im(x))*--(re(x))*sin(re(x))*sinh(im(x))|*cos(x)     //d                                  d                               \                          /d                                  d                               \                       \             //d                                  d                               \                          /d                                  d                               \                       \          3*|||--(im(x))| *sin(re(x))*sinh(im(x)) + ---(im(x))*cosh(im(x))*sin(re(x)) + ---(re(x))*cos(re(x))*sinh(im(x)) - |--(re(x))| *sin(re(x))*sinh(im(x)) + 2*--(im(x))*--(re(x))*cos(re(x))*cosh(im(x))|*sin(re(x))*sinh(im(x)) - ||--(re(x))| *cos(re(x))*cosh(im(x)) + ---(re(x))*cosh(im(x))*sin(re(x)) - |--(im(x))| *cos(re(x))*cosh(im(x)) - ---(im(x))*cos(re(x))*sinh(im(x)) + 2*--(im(x))*--(re(x))*sin(re(x))*sinh(im(x))|*cos(re(x))*cosh(im(x)) + |--(im(x))*cosh(im(x))*sin(re(x)) + --(re(x))*cos(re(x))*sinh(im(x))|*--(im(x))*cosh(im(x))*sin(re(x)) + |--(im(x))*cosh(im(x))*sin(re(x)) + --(re(x))*cos(re(x))*sinh(im(x))|*--(re(x))*cos(re(x))*sinh(im(x)) + |--(re(x))*cosh(im(x))*sin(re(x)) - --(im(x))*cos(re(x))*sinh(im(x))|*--(re(x))*cosh(im(x))*sin(re(x)) - |--(re(x))*cosh(im(x))*sin(re(x)) - --(im(x))*cos(re(x))*sinh(im(x))|*--(im(x))*cos(re(x))*sinh(im(x))|*sin(x)      //d                                  d                               \                          /d                                  d                               \                       \           9*||--(re(x))*cosh(im(x))*sin(re(x)) - --(im(x))*cos(re(x))*sinh(im(x))|*cos(re(x))*cosh(im(x)) - |--(im(x))*cosh(im(x))*sin(re(x)) + --(re(x))*cos(re(x))*sinh(im(x))|*sin(re(x))*sinh(im(x))|*|||--(im(x))| *sin(re(x))*sinh(im(x)) + ---(im(x))*cosh(im(x))*sin(re(x)) + ---(re(x))*cos(re(x))*sinh(im(x)) - |--(re(x))| *sin(re(x))*sinh(im(x)) + 2*--(im(x))*--(re(x))*cos(re(x))*cosh(im(x))|*sin(re(x))*sinh(im(x)) - ||--(re(x))| *cos(re(x))*cosh(im(x)) + ---(re(x))*cosh(im(x))*sin(re(x)) - |--(im(x))| *cos(re(x))*cosh(im(x)) - ---(im(x))*cos(re(x))*sinh(im(x)) + 2*--(im(x))*--(re(x))*sin(re(x))*sinh(im(x))|*cos(re(x))*cosh(im(x)) + |--(im(x))*cosh(im(x))*sin(re(x)) + --(re(x))*cos(re(x))*sinh(im(x))|*--(im(x))*cosh(im(x))*sin(re(x)) + |--(im(x))*cosh(im(x))*sin(re(x)) + --(re(x))*cos(re(x))*sinh(im(x))|*--(re(x))*cos(re(x))*sinh(im(x)) + |--(re(x))*cosh(im(x))*sin(re(x)) - --(im(x))*cos(re(x))*sinh(im(x))|*--(re(x))*cosh(im(x))*sin(re(x)) - |--(re(x))*cosh(im(x))*sin(re(x)) - --(im(x))*cos(re(x))*sinh(im(x))|*--(im(x))*cos(re(x))*sinh(im(x))|*cos(x)         
  ||\dx       /                             3                                   3                                 \dx       /                             \dx       /  dx                                   dx          2                                   \dx       /  dx                                   dx          2                                   dx          2                                   dx          2                              |                          |  3                                 \dx       /                           \dx       /                             3                                   dx          2                                   \dx       /  dx                                   \dx       /  dx                                   dx          2                                   dx          2                                   dx          2                              |                          \dx       /  \dx                                 dx                              /                          \dx       /  \dx                                 dx                              /                          \dx                                 dx                              /   2                                 \dx                                 dx                              /   2                                 \dx                                 dx                              /   2                                 \dx       /  \dx                                 dx                              /                          \dx       /  \dx                                 dx                              /                          \dx                                 dx                              /   2                                   |\dx       /                             2                                 \dx       /                             2                                   dx        dx                              | dx                                   |\dx       /                             2                                   2                                 \dx       /                             dx        dx                              | dx                                   |\dx       /                             2                                   2                                 \dx       /                             dx        dx                              | dx                                   |\dx       /                             2                                 \dx       /                             2                                   dx        dx                              | dx                                   \dx                                 dx                              / dx        dx                                   \dx                                 dx                              / dx        dx                              |          9*||--(re(x))*cosh(im(x))*sin(re(x)) - --(im(x))*cos(re(x))*sinh(im(x))|*cos(re(x))*cosh(im(x)) - |--(im(x))*cosh(im(x))*sin(re(x)) + --(re(x))*cos(re(x))*sinh(im(x))|*sin(re(x))*sinh(im(x))| *sin(x)   3*||--(re(x))*cosh(im(x))*sin(re(x)) - --(im(x))*cos(re(x))*sinh(im(x))|*cos(re(x))*cosh(im(x)) - |--(im(x))*cosh(im(x))*sin(re(x)) + --(re(x))*cos(re(x))*sinh(im(x))|*sin(re(x))*sinh(im(x))|*cos(x)     ||\dx       /                             2                                   2                                 \dx       /                             dx        dx                              |                          |\dx       /                             2                                 \dx       /                             2                                   dx        dx                              |                          \dx                                 dx                              / dx                                 \dx                                 dx                              / dx                                 \dx                                 dx                              / dx                                 \dx                                 dx                              / dx                              |          15*||--(re(x))*cosh(im(x))*sin(re(x)) - --(im(x))*cos(re(x))*sinh(im(x))|*cos(re(x))*cosh(im(x)) - |--(im(x))*cosh(im(x))*sin(re(x)) + --(re(x))*cos(re(x))*sinh(im(x))|*sin(re(x))*sinh(im(x))| *cos(x)     \\dx                                 dx                              /                          \dx                                 dx                              /                       / ||\dx       /                             2                                   2                                 \dx       /                             dx        dx                              |                          |\dx       /                             2                                 \dx       /                             2                                   dx        dx                              |                          \dx                                 dx                              / dx                                 \dx                                 dx                              / dx                                 \dx                                 dx                              / dx                                 \dx                                 dx                              / dx                              |                
  \\                                      dx                                  dx                                                                                                                                      dx                                                                                                dx                                              dx                                              dx                               /                          \dx                                                                                                              dx                                              dx                                                                                                                                                  dx                                              dx                                              dx                               /                                                                                                                                                                                                                                                                                                                        dx                                                                                                        dx                                                                                                        dx                                                                                                                                                                                                                                                                                                                                dx                                    \                                      dx                                                                        dx                                                                              /                                      \                                      dx                                  dx                                                                                                                    /                                      \                                      dx                                  dx                                                                                                                    /                                      \                                      dx                                                                        dx                                                                              /                                                                                                                                                                                                                                                                           /            \\dx                                 dx                              /                          \dx                                 dx                              /                       /             \\dx                                 dx                              /                          \dx                                 dx                              /                       /            \\                                      dx                                  dx                                                                                                                    /                          \                                      dx                                                                        dx                                                                              /                                                                                                                                                                                                                                                                                                                                                                                                                                                           /             \\dx                                 dx                              /                          \dx                                 dx                              /                       /                                                                                                                                                                                                           \\                                      dx                                  dx                                                                                                                    /                          \                                      dx                                                                        dx                                                                              /                                                                                                                                                                                                                                                                                                                                                                                                                                                           /                
- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + sin(x)
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           4                                                                                                                                                                                                        2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        6                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       4                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  |cos(x)|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    |cos(x)|                                                                                                                                                                                                 |cos(x)|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                |cos(x)|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 |cos(x)|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                |cos(x)|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            |cos(x)|
$$\frac{1}{\left|{\cos{\left (x \right )}}\right|} \left(\frac{15 \cos{\left (x \right )}}{\left|{\cos{\left (x \right )}}\right|^{6}} \left(\left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} - \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}\right) \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} - \left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} + \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}\right) \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )}\right)^{3} - \frac{9 \sin{\left (x \right )}}{\left|{\cos{\left (x \right )}}\right|^{4}} \left(\left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} - \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}\right) \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} - \left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} + \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}\right) \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )}\right)^{2} - \frac{9 \cos{\left (x \right )}}{\left|{\cos{\left (x \right )}}\right|^{4}} \left(\left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} - \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}\right) \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} - \left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} + \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}\right) \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )}\right) \left(\left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} - \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}\right) \sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} - \left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} - \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}\right) \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} + \left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} + \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}\right) \sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} + \left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} + \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}\right) \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} + \left(- \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}^{2} + \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}^{2} + \sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d^{2}}{d x^{2}} \Im{x} + \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d^{2}}{d x^{2}} \Re{x} + 2 \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} \frac{d}{d x} \Im{x}\right) \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} - \left(2 \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} \frac{d}{d x} \Im{x} + \sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d^{2}}{d x^{2}} \Re{x} - \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d^{2}}{d x^{2}} \Im{x} + \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}^{2} - \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}^{2}\right) \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )}\right) - \frac{3 \cos{\left (x \right )}}{\left|{\cos{\left (x \right )}}\right|^{2}} \left(\left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} - \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}\right) \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} - \left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} + \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}\right) \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )}\right) + \frac{3 \sin{\left (x \right )}}{\left|{\cos{\left (x \right )}}\right|^{2}} \left(\left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} - \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}\right) \sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} - \left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} - \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}\right) \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} + \left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} + \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}\right) \sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} + \left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} + \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}\right) \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} + \left(- \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}^{2} + \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}^{2} + \sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d^{2}}{d x^{2}} \Im{x} + \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d^{2}}{d x^{2}} \Re{x} + 2 \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} \frac{d}{d x} \Im{x}\right) \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} - \left(2 \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} \frac{d}{d x} \Im{x} + \sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d^{2}}{d x^{2}} \Re{x} - \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d^{2}}{d x^{2}} \Im{x} + \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}^{2} - \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}^{2}\right) \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )}\right) - \frac{\cos{\left (x \right )}}{\left|{\cos{\left (x \right )}}\right|^{2}} \left(2 \left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} - \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}\right) \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} \frac{d}{d x} \Im{x} + \left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} - \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}\right) \sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d^{2}}{d x^{2}} \Re{x} - \left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} - \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}\right) \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d^{2}}{d x^{2}} \Im{x} + \left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} - \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}\right) \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}^{2} - \left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} - \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}\right) \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}^{2} - \left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} + \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}\right) \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}^{2} + \left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} + \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}\right) \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}^{2} + \left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} + \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}\right) \sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d^{2}}{d x^{2}} \Im{x} + \left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} + \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}\right) \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d^{2}}{d x^{2}} \Re{x} + 2 \left(\sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} + \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}\right) \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} \frac{d}{d x} \Im{x} + 2 \left(- \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}^{2} + \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}^{2} + \sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d^{2}}{d x^{2}} \Im{x} + \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d^{2}}{d x^{2}} \Re{x} + 2 \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} \frac{d}{d x} \Im{x}\right) \sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} + 2 \left(- \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}^{2} + \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}^{2} + \sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d^{2}}{d x^{2}} \Im{x} + \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d^{2}}{d x^{2}} \Re{x} + 2 \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} \frac{d}{d x} \Im{x}\right) \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} + 2 \left(2 \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} \frac{d}{d x} \Im{x} + \sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d^{2}}{d x^{2}} \Re{x} - \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d^{2}}{d x^{2}} \Im{x} + \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}^{2} - \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}^{2}\right) \sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} - 2 \left(2 \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} \frac{d}{d x} \Im{x} + \sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d^{2}}{d x^{2}} \Re{x} - \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d^{2}}{d x^{2}} \Im{x} + \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}^{2} - \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}^{2}\right) \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} + \left(- 3 \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} \frac{d^{2}}{d x^{2}} \Re{x} + 3 \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} \frac{d^{2}}{d x^{2}} \Im{x} - 3 \sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}^{2} \frac{d}{d x} \Im{x} + \sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}^{3} + \sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d^{3}}{d x^{3}} \Im{x} - \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}^{3} + 3 \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} \frac{d}{d x} \Im{x}^{2} + \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d^{3}}{d x^{3}} \Re{x} + 3 \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} \frac{d^{2}}{d x^{2}} \Im{x} + 3 \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} \frac{d^{2}}{d x^{2}} \Re{x}\right) \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} - \left(3 \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} \frac{d^{2}}{d x^{2}} \Im{x} + 3 \sin{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} \frac{d^{2}}{d x^{2}} \Re{x} - \sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}^{3} + 3 \sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} \frac{d}{d x} \Im{x}^{2} + \sin{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d^{3}}{d x^{3}} \Re{x} + 3 \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x}^{2} \frac{d}{d x} \Im{x} - \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x}^{3} - \cos{\left (\Re{x} \right )} \sinh{\left (\Im{x} \right )} \frac{d^{3}}{d x^{3}} \Im{x} + 3 \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Re{x} \frac{d^{2}}{d x^{2}} \Re{x} - 3 \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )} \frac{d}{d x} \Im{x} \frac{d^{2}}{d x^{2}} \Im{x}\right) \cos{\left (\Re{x} \right )} \cosh{\left (\Im{x} \right )}\right) + \sin{\left (x \right )}\right)$$
Упростить