Производная 1/(asin(x))^2

Вы ввели

   1    
--------
    2   
asin (x)

$$\frac{1}{\operatorname{asin}^{2}{\left (x \right )}}$$

Первая производная

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

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

Вторая производная

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

$$- \frac{1}{\operatorname{asin}^{3}{\left (x \right )}} \left(\frac{2 x}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{6}{\left(x^{2} - 1\right) \operatorname{asin}{\left (x \right )}}\right)$$

Третья производная

  /                                              2                        \
  |       1                 12                3*x              9*x        |
2*|- ----------- - -------------------- - ----------- + ------------------|
  |          3/2           3/2                    5/2            2        |
  |  /     2\      /     2\        2      /     2\      /      2\         |
  \  \1 - x /      \1 - x /   *asin (x)   \1 - x /      \-1 + x / *asin(x)/
---------------------------------------------------------------------------
                                      3                                    
                                  asin (x)                                 

$$\frac{1}{\operatorname{asin}^{3}{\left (x \right )}} \left(- \frac{6 x^{2}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} + \frac{18 x}{\left(x^{2} - 1\right)^{2} \operatorname{asin}{\left (x \right )}} - \frac{2}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} - \frac{24}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left (x \right )}}\right)$$