Производная 1/(asin(x))

Вы ввели

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

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

                                              2                        
       1                 6                 3*x              6*x        
- ----------- - -------------------- - ----------- + ------------------
          3/2           3/2                    5/2            2        
  /     2\      /     2\        2      /     2\      /      2\         
  \1 - x /      \1 - x /   *asin (x)   \1 - x /      \-1 + x / *asin(x)
-----------------------------------------------------------------------
                                    2                                  
                                asin (x)                               

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