Производная asin(2*x)^(3)

Вы ввели

    3     
asin (2*x)

$$\operatorname{asin}^{3}{\left (2 x \right )}$$

Первая производная

       2     
 6*asin (2*x)
-------------
   __________
  /        2 
\/  1 - 4*x  

$$\frac{6 \operatorname{asin}^{2}{\left (2 x \right )}}{\sqrt{- 4 x^{2} + 1}}$$

Вторая производная

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

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

Третья производная

   /                      2                              2     2     \
   |      2           asin (2*x)    12*x*asin(2*x)   12*x *asin (2*x)|
24*|------------- + ------------- + -------------- + ----------------|
   |          3/2             3/2               2               5/2  |
   |/       2\      /       2\       /        2\      /       2\     |
   \\1 - 4*x /      \1 - 4*x /       \-1 + 4*x /      \1 - 4*x /     /

$$24 \left(\frac{12 x^{2} \operatorname{asin}^{2}{\left (2 x \right )}}{\left(- 4 x^{2} + 1\right)^{\frac{5}{2}}} + \frac{12 x \operatorname{asin}{\left (2 x \right )}}{\left(4 x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}^{2}{\left (2 x \right )}}{\left(- 4 x^{2} + 1\right)^{\frac{3}{2}}} + \frac{2}{\left(- 4 x^{2} + 1\right)^{\frac{3}{2}}}\right)$$