Производная asin(x)^(1/2)

Вы ввели

  _________
\/ asin(x) 

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

                                            2                        
     4                 3                12*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)
---------------------------------------------------------------------
                                _________                            
                            8*\/ asin(x)                             

$$\frac{1}{8 \sqrt{\operatorname{asin}{\left (x \right )}}} \left(\frac{12 x^{2}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} - \frac{6 x}{\left(x^{2} - 1\right)^{2} \operatorname{asin}{\left (x \right )}} + \frac{4}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{3}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left (x \right )}}\right)$$