Производная sqrt(|x|)

Вы ввели

  _____
\/ |x| 

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

                                                                                                                                                                               /           2              2     2                  2             \
                                                                                                                                    3      /d                 d              \ |/d        \    /d        \     d                  d              |
                                                                                                 /d                 d              \    18*|--(im(x))*im(x) + --(re(x))*re(x)|*||--(im(x))|  + |--(re(x))|  + ---(im(x))*im(x) + ---(re(x))*re(x)|
    3                    3                               2                         2          21*|--(im(x))*im(x) + --(re(x))*re(x)|       \dx                dx             / |\dx       /    \dx       /      2                  2             |
   d                    d                    d          d              d          d              \dx                dx             /                                           \                              dx                 dx              /
4*---(im(x))*im(x) + 4*---(re(x))*re(x) + 12*--(im(x))*---(im(x)) + 12*--(re(x))*---(re(x)) + --------------------------------------- - ----------------------------------------------------------------------------------------------------------
    3                    3                   dx          2             dx          2                               4                                                                          2                                                   
  dx                   dx                              dx                        dx                             |x|                                                                        |x|                                                    
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                          3/2                                                                                                                     
                                                                                                                     8*|x|                                                                                                                        

$$\frac{1}{8 \left|{x}\right|^{\frac{3}{2}}} \left(\frac{21}{\left|{x}\right|^{4}} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{3} - \frac{18}{\left|{x}\right|^{2}} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right) \left(\Re{x} \frac{d^{2}}{d x^{2}} \Re{x} + \Im{x} \frac{d^{2}}{d x^{2}} \Im{x} + \frac{d}{d x} \Re{x}^{2} + \frac{d}{d x} \Im{x}^{2}\right) + 4 \Re{x} \frac{d^{3}}{d x^{3}} \Re{x} + 4 \Im{x} \frac{d^{3}}{d x^{3}} \Im{x} + 12 \frac{d}{d x} \Re{x} \frac{d^{2}}{d x^{2}} \Re{x} + 12 \frac{d}{d x} \Im{x} \frac{d^{2}}{d x^{2}} \Im{x}\right)$$