Производная exp(-6*|x|)

Вы ввели

 -6*|x|
e      

$$e^{- 6 \left|{x}\right|}$$

Первая производная

   /d                 d              \  -6*|x|
-6*|--(im(x))*im(x) + --(re(x))*re(x)|*e      
   \dx                dx             /        
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                     |x|                      

$$- \frac{6}{\left|{x}\right|} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right) e^{- 6 \left|{x}\right|}$$

Вторая производная

  /                                                                   2                                                                              2\        
  |                                /d                 d              \                                            /d                 d              \ |        
  |             2              2   |--(im(x))*im(x) + --(re(x))*re(x)|      2                  2                6*|--(im(x))*im(x) + --(re(x))*re(x)| |        
  |  /d        \    /d        \    \dx                dx             /     d                  d                   \dx                dx             / |  -6*|x|
6*|- |--(im(x))|  - |--(re(x))|  + ------------------------------------ - ---(im(x))*im(x) - ---(re(x))*re(x) + --------------------------------------|*e      
  |  \dx       /    \dx       /                       2                     2                  2                                 |x|                  |        
  \                                                |x|                    dx                 dx                                                       /        
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$$\frac{6}{\left|{x}\right|} \left(\frac{6}{\left|{x}\right|} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{2} + \frac{1}{\left|{x}\right|^{2}} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{2} - \Re{x} \frac{d^{2}}{d x^{2}} \Re{x} - \Im{x} \frac{d^{2}}{d x^{2}} \Im{x} - \frac{d}{d x} \Re{x}^{2} - \frac{d}{d x} \Im{x}^{2}\right) e^{- 6 \left|{x}\right|}$$

Третья производная

  /                                                                                                                                                                                                                                                             /           2              2     2                  2             \                                          /           2              2     2                  2             \\        
  |                                                                              3                                         3                                        3                                                       /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)|   18*|--(im(x))*im(x) + --(re(x))*re(x)|*||--(im(x))|  + |--(re(x))|  + ---(im(x))*im(x) + ---(re(x))*re(x)||        
  |    3                  3                36*|--(im(x))*im(x) + --(re(x))*re(x)|    18*|--(im(x))*im(x) + --(re(x))*re(x)|    3*|--(im(x))*im(x) + --(re(x))*re(x)|                  2                        2            \dx                dx             / |\dx       /    \dx       /      2                  2             |      \dx                dx             / |\dx       /    \dx       /      2                  2             ||        
  |   d                  d                    \dx                dx             /       \dx                dx             /      \dx                dx             /      d          d             d          d                                                 \                              dx                 dx              /                                          \                              dx                 dx              /|  -6*|x|
6*|- ---(im(x))*im(x) - ---(re(x))*re(x) - --------------------------------------- - --------------------------------------- - -------------------------------------- - 3*--(im(x))*---(im(x)) - 3*--(re(x))*---(re(x)) + --------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------|*e      
  |    3                  3                                     2                                         3                                        4                      dx          2            dx          2                                                                2                                                                                                        |x|                                                    |        
  \  dx                 dx                                   |x|                                       |x|                                      |x|                                 dx                       dx                                                              |x|                                                                                                                                                                /        
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$$\frac{6}{\left|{x}\right|} \left(- \frac{36}{\left|{x}\right|^{2}} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{3} - \frac{18}{\left|{x}\right|^{3}} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{3} - \frac{3}{\left|{x}\right|^{4}} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{3} + \frac{18}{\left|{x}\right|} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right) \left(\Re{x} \frac{d^{2}}{d x^{2}} \Re{x} + \Im{x} \frac{d^{2}}{d x^{2}} \Im{x} + \frac{d}{d x} \Re{x}^{2} + \frac{d}{d x} \Im{x}^{2}\right) + \frac{3}{\left|{x}\right|^{2}} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right) \left(\Re{x} \frac{d^{2}}{d x^{2}} \Re{x} + \Im{x} \frac{d^{2}}{d x^{2}} \Im{x} + \frac{d}{d x} \Re{x}^{2} + \frac{d}{d x} \Im{x}^{2}\right) - \Re{x} \frac{d^{3}}{d x^{3}} \Re{x} - \Im{x} \frac{d^{3}}{d x^{3}} \Im{x} - 3 \frac{d}{d x} \Re{x} \frac{d^{2}}{d x^{2}} \Re{x} - 3 \frac{d}{d x} \Im{x} \frac{d^{2}}{d x^{2}} \Im{x}\right) e^{- 6 \left|{x}\right|}$$