Производная asin(4*x)^(3)

Вы ввели

    3     
asin (4*x)

$$\operatorname{asin}^{3}{\left (4 x \right )}$$

Первая производная

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

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

Вторая производная

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

$$96 \left(\frac{2 x \operatorname{asin}{\left (4 x \right )}}{\left(- 16 x^{2} + 1\right)^{\frac{3}{2}}} - \frac{1}{16 x^{2} - 1}\right) \operatorname{asin}{\left (4 x \right )}$$

Третья производная

    /                       2                               2     2     \
    |      2            asin (4*x)     24*x*asin(4*x)   48*x *asin (4*x)|
192*|-------------- + -------------- + -------------- + ----------------|
    |           3/2              3/2               2                5/2 |
    |/        2\      /        2\      /         2\      /        2\    |
    \\1 - 16*x /      \1 - 16*x /      \-1 + 16*x /      \1 - 16*x /    /

$$192 \left(\frac{48 x^{2} \operatorname{asin}^{2}{\left (4 x \right )}}{\left(- 16 x^{2} + 1\right)^{\frac{5}{2}}} + \frac{24 x \operatorname{asin}{\left (4 x \right )}}{\left(16 x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}^{2}{\left (4 x \right )}}{\left(- 16 x^{2} + 1\right)^{\frac{3}{2}}} + \frac{2}{\left(- 16 x^{2} + 1\right)^{\frac{3}{2}}}\right)$$