Производная e^(-(|x|))

Вы ввели

 -|x|
E    

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

Первая производная

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

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

Вторая производная

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

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

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

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

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