Производная (x-1)*(|x+2|)

Вы ввели

(x - 1)*|x + 2|

$$\left(x - 1\right) \left|{x + 2}\right|$$

Первая производная

        /            d           d              \          
(x - 1)*|(2 + re(x))*--(re(x)) + --(im(x))*im(x)|          
        \            dx          dx             /          
------------------------------------------------- + |x + 2|
                     |x + 2|                               

$$\frac{1}{\left|{x + 2}\right|} \left(x - 1\right) \left(\left(\Re{x} + 2\right) \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right) + \left|{x + 2}\right|$$

Вторая производная

                                                                                                                                                                            2         
                                                                                                                                   /            d           d              \          
         /           2              2                 2            2             \                                                 |(2 + re(x))*--(re(x)) + --(im(x))*im(x)| *(-1 + x)
         |/d        \    /d        \                 d            d              |                 d             d                 \            dx          dx             /          
(-1 + x)*||--(im(x))|  + |--(re(x))|  + (2 + re(x))*---(re(x)) + ---(im(x))*im(x)| + 2*(2 + re(x))*--(re(x)) + 2*--(im(x))*im(x) - ---------------------------------------------------
         |\dx       /    \dx       /                  2            2             |                 dx            dx                                             2                     
         \                                          dx           dx              /                                                                       |2 + x|                      
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                       |2 + x|                                                                                        

$$\frac{1}{\left|{x + 2}\right|} \left(- \frac{1}{\left|{x + 2}\right|^{2}} \left(x - 1\right) \left(\left(\Re{x} + 2\right) \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{2} + \left(x - 1\right) \left(\left(\Re{x} + 2\right) \frac{d^{2}}{d x^{2}} \Re{x} + \Im{x} \frac{d^{2}}{d x^{2}} \Im{x} + \frac{d}{d x} \Re{x}^{2} + \frac{d}{d x} \Im{x}^{2}\right) + 2 \left(\Re{x} + 2\right) \frac{d}{d x} \Re{x} + 2 \Im{x} \frac{d}{d x} \Im{x}\right)$$

Третья производная

                                                                                                                                                                                                                                                                                                                                                       /           2              2                 2            2             \
                                                                                                                                                                                      2                                                                                              3                       /            d           d              \ |/d        \    /d        \                 d            d              |
                                                                                                                                             /            d           d              \                                                      /            d           d              \             3*(-1 + x)*|(2 + re(x))*--(re(x)) + --(im(x))*im(x)|*||--(im(x))|  + |--(re(x))|  + (2 + re(x))*---(re(x)) + ---(im(x))*im(x)|
             2                2            /              3            3                              2                        2       \   3*|(2 + re(x))*--(re(x)) + --(im(x))*im(x)|                    2              2                3*|(2 + re(x))*--(re(x)) + --(im(x))*im(x)| *(-1 + x)              \            dx          dx             / |\dx       /    \dx       /                  2            2             |
  /d        \      /d        \             |             d            d                   d          d             d          d        |     \            dx          dx             /                   d              d                   \            dx          dx             /                                                                  \                                          dx           dx              /
3*|--(im(x))|  + 3*|--(re(x))|  + (-1 + x)*|(2 + re(x))*---(re(x)) + ---(im(x))*im(x) + 3*--(im(x))*---(im(x)) + 3*--(re(x))*---(re(x))| - -------------------------------------------- + 3*(2 + re(x))*---(re(x)) + 3*---(im(x))*im(x) + ----------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------
  \dx       /      \dx       /             |              3            3                  dx          2            dx          2       |                            2                                     2              2                                              4                                                                                           2                                                           
                                           \            dx           dx                             dx                       dx        /                     |2 + x|                                    dx             dx                                        |2 + x|                                                                                     |2 + x|                                                            
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                            |2 + x|                                                                                                                                                                                                             

$$\frac{1}{\left|{x + 2}\right|} \left(\frac{3}{\left|{x + 2}\right|^{4}} \left(x - 1\right) \left(\left(\Re{x} + 2\right) \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{3} - \frac{3}{\left|{x + 2}\right|^{2}} \left(x - 1\right) \left(\left(\Re{x} + 2\right) \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right) \left(\left(\Re{x} + 2\right) \frac{d^{2}}{d x^{2}} \Re{x} + \Im{x} \frac{d^{2}}{d x^{2}} \Im{x} + \frac{d}{d x} \Re{x}^{2} + \frac{d}{d x} \Im{x}^{2}\right) + \left(x - 1\right) \left(\left(\Re{x} + 2\right) \frac{d^{3}}{d x^{3}} \Re{x} + \Im{x} \frac{d^{3}}{d x^{3}} \Im{x} + 3 \frac{d}{d x} \Re{x} \frac{d^{2}}{d x^{2}} \Re{x} + 3 \frac{d}{d x} \Im{x} \frac{d^{2}}{d x^{2}} \Im{x}\right) - \frac{3}{\left|{x + 2}\right|^{2}} \left(\left(\Re{x} + 2\right) \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{2} + 3 \left(\Re{x} + 2\right) \frac{d^{2}}{d x^{2}} \Re{x} + 3 \Im{x} \frac{d^{2}}{d x^{2}} \Im{x} + 3 \frac{d}{d x} \Re{x}^{2} + 3 \frac{d}{d x} \Im{x}^{2}\right)$$