Производная (asin(x)^(-1/2))

Вы ввели

     1     
-----------
  _________
\/ asin(x) 

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

Первая производная

          -1            
------------------------
     ________           
    /      2      3/2   
2*\/  1 - x  *asin   (x)

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

Вторая производная

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

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

Третья производная

                                              2                        
       4                 15               12*x              18*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)
-----------------------------------------------------------------------
                                    3/2                                
                              8*asin   (x)                             

$$\frac{1}{8 \operatorname{asin}^{\frac{3}{2}}{\left (x \right )}} \left(- \frac{12 x^{2}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} + \frac{18 x}{\left(x^{2} - 1\right)^{2} \operatorname{asin}{\left (x \right )}} - \frac{4}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} - \frac{15}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left (x \right )}}\right)$$