Производная asin(sin(x))

Вы ввели

asin(sin(x))

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

Первая производная

     cos(x)     
----------------
   _____________
  /        2    
\/  1 - sin (x) 

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

Вторая производная

/          2     \       
|       cos (x)  |       
|-1 + -----------|*sin(x)
|            2   |       
\     1 - sin (x)/       
-------------------------
        _____________    
       /        2        
     \/  1 - sin (x)     

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

Третья производная

/          2              2            2       2   \       
|       cos (x)      3*sin (x)    3*cos (x)*sin (x)|       
|-1 + ----------- - ----------- + -----------------|*cos(x)
|            2             2                     2 |       
|     1 - sin (x)   1 - sin (x)     /       2   \  |       
\                                   \1 - sin (x)/  /       
-----------------------------------------------------------
                         _____________                     
                        /        2                         
                      \/  1 - sin (x)                      

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

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