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)                                 

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