Производная asin(x)^(1/3)

Вы ввели

3 _________
\/ asin(x) 

$$\sqrt[3]{\operatorname{asin}{\left (x \right )}}$$

Первая производная

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

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

Вторая производная

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

$$\frac{1}{9 \operatorname{asin}^{\frac{2}{3}}{\left (x \right )}} \left(\frac{3 x}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{2}{\left(x^{2} - 1\right) \operatorname{asin}{\left (x \right )}}\right)$$

Третья производная

                      2                                                     
      1              x                   10                     2*x         
------------- + ----------- + ----------------------- - --------------------
          3/2           5/2              3/2                       2        
  /     2\      /     2\         /     2\        2        /      2\         
3*\1 - x /      \1 - x /      27*\1 - x /   *asin (x)   3*\-1 + x / *asin(x)
----------------------------------------------------------------------------
                                     2/3                                    
                                 asin   (x)                                 

$$\frac{1}{\operatorname{asin}^{\frac{2}{3}}{\left (x \right )}} \left(\frac{x^{2}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} - \frac{2 x}{3 \left(x^{2} - 1\right)^{2} \operatorname{asin}{\left (x \right )}} + \frac{1}{3 \left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{10}{27 \left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left (x \right )}}\right)$$