Производная функции/ От одной переменной/ y' = (sin(|x|)-(|x|))'

Производная sin(|x|)-(|x|)

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Решение

Вы ввели [src]
sin(|x|) - |x|
sin⁡(∣x∣)−∣x∣\sin{\left (\left|{x}\right| \right )} - \left|{x}\right|
Первая производная [src]
  d                 d                 /d                 d              \         
  --(im(x))*im(x) + --(re(x))*re(x)   |--(im(x))*im(x) + --(re(x))*re(x)|*cos(|x|)
  dx                dx                \dx                dx             /         
- --------------------------------- + --------------------------------------------
                 |x|                                      |x|
1∣x∣(ℜxddxℜx+ℑxddxℑx)cos⁡(∣x∣)−1∣x∣(ℜxddxℜx+ℑxddxℑx)\frac{1}{\left|{x}\right|} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right) \cos{\left (\left|{x}\right| \right )} - \frac{1}{\left|{x}\right|} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)
Упростить
Вторая производная [src]
                                                                   2                                                                                                                                                           2                                               2         
                                /d                 d              \                                                                                                                         /d                 d              \             /d                 d              \          
             2              2   |--(im(x))*im(x) + --(re(x))*re(x)|    /           2              2     2                  2             \              2                  2                |--(im(x))*im(x) + --(re(x))*re(x)| *sin(|x|)   |--(im(x))*im(x) + --(re(x))*re(x)| *cos(|x|)
  /d        \    /d        \    \dx                dx             /    |/d        \    /d        \     d                  d              |             d                  d                 \dx                dx             /             \dx                dx             /          
- |--(im(x))|  - |--(re(x))|  + ------------------------------------ + ||--(im(x))|  + |--(re(x))|  + ---(im(x))*im(x) + ---(re(x))*re(x)|*cos(|x|) - ---(im(x))*im(x) - ---(re(x))*re(x) - --------------------------------------------- - ---------------------------------------------
  \dx       /    \dx       /                       2                   |\dx       /    \dx       /      2                  2             |              2                  2                                     |x|                                                2                    
                                                |x|                    \                              dx                 dx              /            dx                 dx                                                                                      |x|                     
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                           |x|
1∣x∣(−1∣x∣(ℜxddxℜx+ℑxddxℑx)2sin⁡(∣x∣)−1∣x∣2(ℜxddxℜx+ℑxddxℑx)2cos⁡(∣x∣)+1∣x∣2(ℜxddxℜx+ℑxddxℑx)2+(ℜxd2dx2ℜx+ℑxd2dx2ℑx+ddxℜx2+ddxℑx2)cos⁡(∣x∣)−ℜxd2dx2ℜx−ℑxd2dx2ℑx−ddxℜx2−ddxℑx2)\frac{1}{\left|{x}\right|} \left(- \frac{1}{\left|{x}\right|} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{2} \sin{\left (\left|{x}\right| \right )} - \frac{1}{\left|{x}\right|^{2}} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{2} \cos{\left (\left|{x}\right| \right )} + \frac{1}{\left|{x}\right|^{2}} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{2} + \left(\Re{x} \frac{d^{2}}{d x^{2}} \Re{x} + \Im{x} \frac{d^{2}}{d x^{2}} \Im{x} + \frac{d}{d x} \Re{x}^{2} + \frac{d}{d x} \Im{x}^{2}\right) \cos{\left (\left|{x}\right| \right )} - \Re{x} \frac{d^{2}}{d x^{2}} \Re{x} - \Im{x} \frac{d^{2}}{d x^{2}} \Im{x} - \frac{d}{d x} \Re{x}^{2} - \frac{d}{d x} \Im{x}^{2}\right)
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Третья производная [src]
                                                                                                                                                                                                                                                                                                                                                                                                                              /           2              2     2                  2             \                                         /           2              2     2                  2             \                                                  /           2              2     2                  2             \         
                                                                                                                                                                              3                                                                                        3                                                 3                                                 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              \             3*|--(im(x))*im(x) + --(re(x))*re(x)|*||--(im(x))|  + |--(re(x))|  + ---(im(x))*im(x) + ---(re(x))*re(x)|   3*|--(im(x))*im(x) + --(re(x))*re(x)|*||--(im(x))|  + |--(re(x))|  + ---(im(x))*im(x) + ---(re(x))*re(x)|*sin(|x|)   3*|--(im(x))*im(x) + --(re(x))*re(x)|*||--(im(x))|  + |--(re(x))|  + ---(im(x))*im(x) + ---(re(x))*re(x)|*cos(|x|)
/  3                  3                              2                        2       \              3                  3                3*|--(im(x))*im(x) + --(re(x))*re(x)|                  2                        2          |--(im(x))*im(x) + --(re(x))*re(x)| *cos(|x|)   3*|--(im(x))*im(x) + --(re(x))*re(x)| *cos(|x|)   3*|--(im(x))*im(x) + --(re(x))*re(x)| *sin(|x|)     \dx                dx             / |\dx       /    \dx       /      2                  2             |     \dx                dx             / |\dx       /    \dx       /      2                  2             |              \dx                dx             / |\dx       /    \dx       /      2                  2             |         
| d                  d                   d          d             d          d        |             d                  d                   \dx                dx             /      d          d             d          d           \dx                dx             /               \dx                dx             /               \dx                dx             /                                                   \                              dx                 dx              /                                         \                              dx                 dx              /                                                  \                              dx                 dx              /         
|---(im(x))*im(x) + ---(re(x))*re(x) + 3*--(im(x))*---(im(x)) + 3*--(re(x))*---(re(x))|*cos(|x|) - ---(im(x))*im(x) - ---(re(x))*re(x) - -------------------------------------- - 3*--(im(x))*---(im(x)) - 3*--(re(x))*---(re(x)) - --------------------------------------------- + ----------------------------------------------- + ----------------------------------------------- + --------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------
|  3                  3                  dx          2            dx          2       |              3                  3                                    4                      dx          2            dx          2                                  2                                                4                                                 3                                                                              2                                                                                                            |x|                                                                                                                     2                                                       
\dx                 dx                             dx                       dx        /            dx                 dx                                  |x|                                 dx                       dx                                |x|                                              |x|                                               |x|                                                                            |x|                                                                                                                                                                                                                                  |x|                                                        
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                                                                                                                    |x|
1∣x∣(3∣x∣3(ℜxddxℜx+ℑxddxℑx)3sin⁡(∣x∣)−1∣x∣2(ℜxddxℜx+ℑxddxℑx)3cos⁡(∣x∣)+3∣x∣4(ℜxddxℜx+ℑxddxℑx)3cos⁡(∣x∣)−3∣x∣4(ℜxddxℜx+ℑxddxℑx)3−3∣x∣(ℜxddxℜx+ℑxddxℑx)(ℜxd2dx2ℜx+ℑxd2dx2ℑx+ddxℜx2+ddxℑx2)sin⁡(∣x∣)−3∣x∣2(ℜxddxℜx+ℑxddxℑx)(ℜxd2dx2ℜx+ℑxd2dx2ℑx+ddxℜx2+ddxℑx2)cos⁡(∣x∣)+3∣x∣2(ℜxddxℜx+ℑxddxℑx)(ℜxd2dx2ℜx+ℑxd2dx2ℑx+ddxℜx2+ddxℑx2)+(ℜxd3dx3ℜx+ℑxd3dx3ℑx+3ddxℜxd2dx2ℜx+3ddxℑxd2dx2ℑx)cos⁡(∣x∣)−ℜxd3dx3ℜx−ℑxd3dx3ℑx−3ddxℜxd2dx2ℜx−3ddxℑxd2dx2ℑx)\frac{1}{\left|{x}\right|} \left(\frac{3}{\left|{x}\right|^{3}} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{3} \sin{\left (\left|{x}\right| \right )} - \frac{1}{\left|{x}\right|^{2}} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{3} \cos{\left (\left|{x}\right| \right )} + \frac{3}{\left|{x}\right|^{4}} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{3} \cos{\left (\left|{x}\right| \right )} - \frac{3}{\left|{x}\right|^{4}} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{3} - \frac{3}{\left|{x}\right|} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right) \left(\Re{x} \frac{d^{2}}{d x^{2}} \Re{x} + \Im{x} \frac{d^{2}}{d x^{2}} \Im{x} + \frac{d}{d x} \Re{x}^{2} + \frac{d}{d x} \Im{x}^{2}\right) \sin{\left (\left|{x}\right| \right )} - \frac{3}{\left|{x}\right|^{2}} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right) \left(\Re{x} \frac{d^{2}}{d x^{2}} \Re{x} + \Im{x} \frac{d^{2}}{d x^{2}} \Im{x} + \frac{d}{d x} \Re{x}^{2} + \frac{d}{d x} \Im{x}^{2}\right) \cos{\left (\left|{x}\right| \right )} + \frac{3}{\left|{x}\right|^{2}} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right) \left(\Re{x} \frac{d^{2}}{d x^{2}} \Re{x} + \Im{x} \frac{d^{2}}{d x^{2}} \Im{x} + \frac{d}{d x} \Re{x}^{2} + \frac{d}{d x} \Im{x}^{2}\right) + \left(\Re{x} \frac{d^{3}}{d x^{3}} \Re{x} + \Im{x} \frac{d^{3}}{d x^{3}} \Im{x} + 3 \frac{d}{d x} \Re{x} \frac{d^{2}}{d x^{2}} \Re{x} + 3 \frac{d}{d x} \Im{x} \frac{d^{2}}{d x^{2}} \Im{x}\right) \cos{\left (\left|{x}\right| \right )} - \Re{x} \frac{d^{3}}{d x^{3}} \Re{x} - \Im{x} \frac{d^{3}}{d x^{3}} \Im{x} - 3 \frac{d}{d x} \Re{x} \frac{d^{2}}{d x^{2}} \Re{x} - 3 \frac{d}{d x} \Im{x} \frac{d^{2}}{d x^{2}} \Im{x}\right)
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