Производная 2^(x*asin(x))

Вы ввели

 x*asin(x)
2         

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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