Производная sqrt(1-asin(x))

Вы ввели

  _____________
\/ 1 - asin(x) 

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

Первая производная

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

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

Вторая производная

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

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

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 /   *(1 - asin(x))    \1 - x /      (1 - asin(x))*\-1 + x / / 
-------------------------------------------------------------------------------------
                                      _____________                                  
                                  8*\/ 1 - asin(x)                                   

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