Производная (asin(x))^e^x

Вы ввели

         / x\
         \E /
(asin(x))    

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

Подробное решение

1. Не могу найти шаги в поиске этой производной.

   Но производная

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

2. Теперь упростим:

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

---

Ответ:

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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