Производная (asin(x))^(x^2)

Вы ввели

         / 2\
         \x /
(asin(x))    

$$\operatorname{asin}^{x^{2}}{\left (x \right )}$$

Подробное решение

1. Не могу найти шаги в поиске этой производной.

   Но производная

   $\left(\log{\left (x^{2} \right )} + 1\right) \left(x^{2}\right)^{x^{2}}$

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Ответ:

$\left(\log{\left (x^{2} \right )} + 1\right) \left(x^{2}\right)^{x^{2}}$

Первая производная

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

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

Вторая производная

         / 2\ /                                                          2            2                     3                              \
         \x / |                  2 /                          x         \            x                     x                    4*x        |
(asin(x))    *|2*log(asin(x)) + x *|2*log(asin(x)) + -------------------|  + ------------------ + ------------------- + -------------------|
              |                    |                    ________        |    /      2\     2              3/2              ________        |
              |                    |                   /      2         |    \-1 + x /*asin (x)   /     2\                /      2         |
              \                    \                 \/  1 - x  *asin(x)/                         \1 - x /   *asin(x)   \/  1 - x  *asin(x)/

$$\left(\frac{x^{3}}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{asin}{\left (x \right )}} + x^{2} \left(\frac{x}{\sqrt{- x^{2} + 1} \operatorname{asin}{\left (x \right )}} + 2 \log{\left (\operatorname{asin}{\left (x \right )} \right )}\right)^{2} + \frac{x^{2}}{\left(x^{2} - 1\right) \operatorname{asin}^{2}{\left (x \right )}} + \frac{4 x}{\sqrt{- x^{2} + 1} \operatorname{asin}{\left (x \right )}} + 2 \log{\left (\operatorname{asin}{\left (x \right )} \right )}\right) \operatorname{asin}^{x^{2}}{\left (x \right )}$$

Третья производная

              /                                                                  4             2                3                     2                                                                                                                                                           \
              |                                                  6            3*x           7*x              3*x                   2*x                   6*x                                                                                                                                      |
              |                                             ----------- + ----------- + ----------- - ------------------ + -------------------- + -----------------                                                                                                                               |
              |                                                ________           5/2           3/2            2                   3/2            /      2\                                                                                                                                       |
         / 2\ |                                         3     /      2    /     2\      /     2\      /      2\            /     2\        2      \-1 + x /*asin(x)                                              /                          2                     3                              \|
         \x / | 3 /                          x         \    \/  1 - x     \1 - x /      \1 - x /      \-1 + x / *asin(x)   \1 - x /   *asin (x)                           /                          x         \ |                         x                     x                    4*x        ||
(asin(x))    *|x *|2*log(asin(x)) + -------------------|  + ------------------------------------------------------------------------------------------------------- + 3*x*|2*log(asin(x)) + -------------------|*|2*log(asin(x)) + ------------------ + ------------------- + -------------------||
              |   |                    ________        |                                                    asin(x)                                                       |                    ________        | |                 /      2\     2              3/2              ________        ||
              |   |                   /      2         |                                                                                                                  |                   /      2         | |                 \-1 + x /*asin (x)   /     2\                /      2         ||
              \   \                 \/  1 - x  *asin(x)/                                                                                                                  \                 \/  1 - x  *asin(x)/ \                                      \1 - x /   *asin(x)   \/  1 - x  *asin(x)//

$$\left(x^{3} \left(\frac{x}{\sqrt{- x^{2} + 1} \operatorname{asin}{\left (x \right )}} + 2 \log{\left (\operatorname{asin}{\left (x \right )} \right )}\right)^{3} + 3 x \left(\frac{x}{\sqrt{- x^{2} + 1} \operatorname{asin}{\left (x \right )}} + 2 \log{\left (\operatorname{asin}{\left (x \right )} \right )}\right) \left(\frac{x^{3}}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{asin}{\left (x \right )}} + \frac{x^{2}}{\left(x^{2} - 1\right) \operatorname{asin}^{2}{\left (x \right )}} + \frac{4 x}{\sqrt{- x^{2} + 1} \operatorname{asin}{\left (x \right )}} + 2 \log{\left (\operatorname{asin}{\left (x \right )} \right )}\right) + \frac{1}{\operatorname{asin}{\left (x \right )}} \left(\frac{3 x^{4}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} - \frac{3 x^{3}}{\left(x^{2} - 1\right)^{2} \operatorname{asin}{\left (x \right )}} + \frac{7 x^{2}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{2 x^{2}}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left (x \right )}} + \frac{6 x}{\left(x^{2} - 1\right) \operatorname{asin}{\left (x \right )}} + \frac{6}{\sqrt{- x^{2} + 1}}\right)\right) \operatorname{asin}^{x^{2}}{\left (x \right )}$$