Производная (asin(x)^6)/6

Вы ввели

    6   
asin (x)
--------
   6    

$$\frac{1}{6} \operatorname{asin}^{6}{\left (x \right )}$$

Первая производная

      5    
  asin (x) 
-----------
   ________
  /      2 
\/  1 - x  

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

Вторая производная

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

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

Третья производная

         /                    2          2     2                  \
    3    |     20         asin (x)    3*x *asin (x)   15*x*asin(x)|
asin (x)*|----------- + ----------- + ------------- + ------------|
         |        3/2           3/2            5/2              2 |
         |/     2\      /     2\       /     2\        /      2\  |
         \\1 - x /      \1 - x /       \1 - x /        \-1 + x /  /

$$\left(\frac{3 x^{2} \operatorname{asin}^{2}{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} + \frac{15 x \operatorname{asin}{\left (x \right )}}{\left(x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}^{2}{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{20}{\left(- x^{2} + 1\right)^{\frac{3}{2}}}\right) \operatorname{asin}^{3}{\left (x \right )}$$