Производная (asin(x)+x)^5

Вы ввели

             5
(asin(x) + x) 

$$\left(x + \operatorname{asin}{\left (x \right )}\right)^{5}$$

Первая производная

             4 /         5     \
(asin(x) + x) *|5 + -----------|
               |       ________|
               |      /      2 |
               \    \/  1 - x  /

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

Вторая производная

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

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

Третья производная

                 /                                                                    /         1     \              \
                 |                                                               12*x*|1 + -----------|*(x + asin(x))|
                 |                                                                    |       ________|              |
                 |                    3                2      2              2        |      /      2 |              |
               2 |   /         1     \    (x + asin(x))    3*x *(x + asin(x))         \    \/  1 - x  /              |
5*(x + asin(x)) *|12*|1 + -----------|  + -------------- + ------------------- + ------------------------------------|
                 |   |       ________|             3/2                 5/2                           3/2             |
                 |   |      /      2 |     /     2\            /     2\                      /     2\                |
                 \   \    \/  1 - x  /     \1 - x /            \1 - x /                      \1 - x /                /

$$5 \left(x + \operatorname{asin}{\left (x \right )}\right)^{2} \left(\frac{3 x^{2} \left(x + \operatorname{asin}{\left (x \right )}\right)^{2}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} + \frac{12 x}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} \left(1 + \frac{1}{\sqrt{- x^{2} + 1}}\right) \left(x + \operatorname{asin}{\left (x \right )}\right) + 12 \left(1 + \frac{1}{\sqrt{- x^{2} + 1}}\right)^{3} + \frac{\left(x + \operatorname{asin}{\left (x \right )}\right)^{2}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}}\right)$$