Производная (|x|)

Вы ввели

|x|

$$\left|{x}\right|$$

Первая производная

d                 d              
--(im(x))*im(x) + --(re(x))*re(x)
dx                dx             
---------------------------------
               |x|               

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

Третья производная

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

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