Производная asin(4*x)^5

Вы ввели

    5     
asin (4*x)

$$\operatorname{asin}^{5}{\left (4 x \right )}$$

Первая производная

       4      
20*asin (4*x) 
--------------
   ___________
  /         2 
\/  1 - 16*x  

$$\frac{20 \operatorname{asin}^{4}{\left (4 x \right )}}{\sqrt{- 16 x^{2} + 1}}$$

Вторая производная

        3      /      1         x*asin(4*x)  \
320*asin (4*x)*|- ---------- + --------------|
               |           2              3/2|
               |  -1 + 16*x    /        2\   |
               \               \1 - 16*x /   /

$$320 \left(\frac{x \operatorname{asin}{\left (4 x \right )}}{\left(- 16 x^{2} + 1\right)^{\frac{3}{2}}} - \frac{1}{16 x^{2} - 1}\right) \operatorname{asin}^{3}{\left (4 x \right )}$$

Третья производная

               /                       2                               2     2     \
        2      |      12           asin (4*x)     48*x*asin(4*x)   48*x *asin (4*x)|
320*asin (4*x)*|-------------- + -------------- + -------------- + ----------------|
               |           3/2              3/2               2                5/2 |
               |/        2\      /        2\      /         2\      /        2\    |
               \\1 - 16*x /      \1 - 16*x /      \-1 + 16*x /      \1 - 16*x /    /

$$320 \left(\frac{48 x^{2} \operatorname{asin}^{2}{\left (4 x \right )}}{\left(- 16 x^{2} + 1\right)^{\frac{5}{2}}} + \frac{48 x \operatorname{asin}{\left (4 x \right )}}{\left(16 x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}^{2}{\left (4 x \right )}}{\left(- 16 x^{2} + 1\right)^{\frac{3}{2}}} + \frac{12}{\left(- 16 x^{2} + 1\right)^{\frac{3}{2}}}\right) \operatorname{asin}^{2}{\left (4 x \right )}$$