Производная 2^|x|

Вы ввели

 |x|
2   

$$2^{\left|{x}\right|}$$

Первая производная

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

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

Вторая производная

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

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

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              \     2        /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)|*log(2)|       
     |  3                  3                3*|--(im(x))*im(x) + --(re(x))*re(x)|                  2                        2          |--(im(x))*im(x) + --(re(x))*re(x)| *log (2)   3*|--(im(x))*im(x) + --(re(x))*re(x)| *log(2)     \dx                dx             / |\dx       /    \dx       /      2                  2             |     \dx                dx             / |\dx       /    \dx       /      2                  2             |       |       
 |x| | d                  d                   \dx                dx             /      d          d             d          d           \dx                dx             /              \dx                dx             /                                                 \                              dx                 dx              /                                         \                              dx                 dx              /       |       
2   *|---(im(x))*im(x) + ---(re(x))*re(x) + -------------------------------------- + 3*--(im(x))*---(im(x)) + 3*--(re(x))*---(re(x)) + -------------------------------------------- - --------------------------------------------- - --------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------|*log(2)
     |  3                  3                                    4                      dx          2            dx          2                                 2                                               3                                                                             2                                                                                                           |x|                                                       |       
     \dx                 dx                                  |x|                                 dx                       dx                               |x|                                             |x|                                                                           |x|                                                                                                                                                                      /       
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$$\frac{2^{\left|{x}\right|}}{\left|{x}\right|} \left(\frac{1}{\left|{x}\right|^{2}} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{3} \log^{2}{\left (2 \right )} - \frac{3}{\left|{x}\right|^{3}} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{3} \log{\left (2 \right )} + \frac{3}{\left|{x}\right|^{4}} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right)^{3} + \frac{3}{\left|{x}\right|} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right) \left(\Re{x} \frac{d^{2}}{d x^{2}} \Re{x} + \Im{x} \frac{d^{2}}{d x^{2}} \Im{x} + \frac{d}{d x} \Re{x}^{2} + \frac{d}{d x} \Im{x}^{2}\right) \log{\left (2 \right )} - \frac{3}{\left|{x}\right|^{2}} \left(\Re{x} \frac{d}{d x} \Re{x} + \Im{x} \frac{d}{d x} \Im{x}\right) \left(\Re{x} \frac{d^{2}}{d x^{2}} \Re{x} + \Im{x} \frac{d^{2}}{d x^{2}} \Im{x} + \frac{d}{d x} \Re{x}^{2} + \frac{d}{d x} \Im{x}^{2}\right) + \Re{x} \frac{d^{3}}{d x^{3}} \Re{x} + \Im{x} \frac{d^{3}}{d x^{3}} \Im{x} + 3 \frac{d}{d x} \Re{x} \frac{d^{2}}{d x^{2}} \Re{x} + 3 \frac{d}{d x} \Im{x} \frac{d^{2}}{d x^{2}} \Im{x}\right) \log{\left (2 \right )}$$