Производная (asin(8*x))^5

Вы ввели

    5     
asin (8*x)

$$\operatorname{asin}^{5}{\left (8 x \right )}$$

Первая производная

       4      
40*asin (8*x) 
--------------
   ___________
  /         2 
\/  1 - 64*x  

$$\frac{40 \operatorname{asin}^{4}{\left (8 x \right )}}{\sqrt{- 64 x^{2} + 1}}$$

Вторая производная

         3      /      1        2*x*asin(8*x) \
1280*asin (8*x)*|- ---------- + --------------|
                |           2              3/2|
                |  -1 + 64*x    /        2\   |
                \               \1 - 64*x /   /

$$1280 \left(\frac{2 x \operatorname{asin}{\left (8 x \right )}}{\left(- 64 x^{2} + 1\right)^{\frac{3}{2}}} - \frac{1}{64 x^{2} - 1}\right) \operatorname{asin}^{3}{\left (8 x \right )}$$

Третья производная

                /                       2                                2     2     \
         2      |      12           asin (8*x)     96*x*asin(8*x)   192*x *asin (8*x)|
2560*asin (8*x)*|-------------- + -------------- + -------------- + -----------------|
                |           3/2              3/2               2                 5/2 |
                |/        2\      /        2\      /         2\       /        2\    |
                \\1 - 64*x /      \1 - 64*x /      \-1 + 64*x /       \1 - 64*x /    /

$$2560 \left(\frac{192 x^{2} \operatorname{asin}^{2}{\left (8 x \right )}}{\left(- 64 x^{2} + 1\right)^{\frac{5}{2}}} + \frac{96 x \operatorname{asin}{\left (8 x \right )}}{\left(64 x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}^{2}{\left (8 x \right )}}{\left(- 64 x^{2} + 1\right)^{\frac{3}{2}}} + \frac{12}{\left(- 64 x^{2} + 1\right)^{\frac{3}{2}}}\right) \operatorname{asin}^{2}{\left (8 x \right )}$$