Производная x^(exp(asin(x)))

Вы ввели

 / asin(x)\
 \e       /
x          

$$x^{e^{\operatorname{asin}{\left (x \right )}}}$$

Подробное решение

1. Не могу найти шаги в поиске этой производной.

   Но производная

   $\left(\log{\left (e^{\operatorname{asin}{\left (x \right )}} \right )} + 1\right) \left(e^{\operatorname{asin}{\left (x \right )}}\right)^{e^{\operatorname{asin}{\left (x \right )}}}$

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Ответ:

$\left(\log{\left (e^{\operatorname{asin}{\left (x \right )}} \right )} + 1\right) \left(e^{\operatorname{asin}{\left (x \right )}}\right)^{e^{\operatorname{asin}{\left (x \right )}}}$

Первая производная

 / asin(x)\ / asin(x)    asin(x)       \
 \e       / |e          e       *log(x)|
x          *|-------- + ---------------|
            |   x            ________  |
            |               /      2   |
            \             \/  1 - x    /

$$x^{e^{\operatorname{asin}{\left (x \right )}}} \left(\frac{e^{\operatorname{asin}{\left (x \right )}} \log{\left (x \right )}}{\sqrt{- x^{2} + 1}} + \frac{1}{x} e^{\operatorname{asin}{\left (x \right )}}\right)$$

Вторая производная

 / asin(x)\ /                        2                                                 \         
 \e       / |  1    /1      log(x)  \   asin(x)    log(x)         2           x*log(x) |  asin(x)
x          *|- -- + |- + -----------| *e        - ------- + ------------- + -----------|*e       
            |   2   |x      ________|                   2        ________           3/2|         
            |  x    |      /      2 |             -1 + x        /      2    /     2\   |         
            \       \    \/  1 - x  /                       x*\/  1 - x     \1 - x /   /         

$$x^{e^{\operatorname{asin}{\left (x \right )}}} \left(\frac{x \log{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \left(\frac{\log{\left (x \right )}}{\sqrt{- x^{2} + 1}} + \frac{1}{x}\right)^{2} e^{\operatorname{asin}{\left (x \right )}} - \frac{\log{\left (x \right )}}{x^{2} - 1} + \frac{2}{x \sqrt{- x^{2} + 1}} - \frac{1}{x^{2}}\right) e^{\operatorname{asin}{\left (x \right )}}$$

Третья производная

 / asin(x)\ /                                    3                                                                           2                                                                                     \         
 \e       / |2         3        /1      log(x)  \   2*asin(x)        3              3            2*log(x)    3*x*log(x)   3*x *log(x)     /1      log(x)  \ /  1     log(x)         2           x*log(x) \  asin(x)|  asin(x)
x          *|-- + ----------- + |- + -----------| *e          - ----------- - -------------- + ----------- + ---------- + ----------- + 3*|- + -----------|*|- -- - ------- + ------------- + -----------|*e       |*e       
            | 3           3/2   |x      ________|                 /      2\         ________           3/2            2           5/2     |x      ________| |   2         2        ________           3/2|         |         
            |x    /     2\      |      /      2 |               x*\-1 + x /    2   /      2    /     2\      /      2\    /     2\        |      /      2 | |  x    -1 + x        /      2    /     2\   |         |         
            \     \1 - x /      \    \/  1 - x  /                             x *\/  1 - x     \1 - x /      \-1 + x /    \1 - x /        \    \/  1 - x  / \                 x*\/  1 - x     \1 - x /   /         /         

$$x^{e^{\operatorname{asin}{\left (x \right )}}} \left(\frac{3 x^{2} \log{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} + \frac{3 x \log{\left (x \right )}}{\left(x^{2} - 1\right)^{2}} + \left(\frac{\log{\left (x \right )}}{\sqrt{- x^{2} + 1}} + \frac{1}{x}\right)^{3} e^{2 \operatorname{asin}{\left (x \right )}} + 3 \left(\frac{\log{\left (x \right )}}{\sqrt{- x^{2} + 1}} + \frac{1}{x}\right) \left(\frac{x \log{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} - \frac{\log{\left (x \right )}}{x^{2} - 1} + \frac{2}{x \sqrt{- x^{2} + 1}} - \frac{1}{x^{2}}\right) e^{\operatorname{asin}{\left (x \right )}} + \frac{2 \log{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{3}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} - \frac{3}{x \left(x^{2} - 1\right)} - \frac{3}{x^{2} \sqrt{- x^{2} + 1}} + \frac{2}{x^{3}}\right) e^{\operatorname{asin}{\left (x \right )}}$$