Производная asin(a*sin(x))

Вы ввели

asin(a*sin(x))

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

Первая производная

      a*cos(x)     
-------------------
   ________________
  /      2    2    
\/  1 - a *sin (x) 

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

Вторая производная

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

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

Третья производная

  /        2    2            2    2          4    2       2   \       
  |       a *cos (x)      3*a *sin (x)    3*a *cos (x)*sin (x)|       
a*|-1 + -------------- - -------------- + --------------------|*cos(x)
  |          2    2           2    2                       2  |       
  |     1 - a *sin (x)   1 - a *sin (x)    /     2    2   \   |       
  \                                        \1 - a *sin (x)/   /       
----------------------------------------------------------------------
                            ________________                          
                           /      2    2                              
                         \/  1 - a *sin (x)                           

$$\frac{a \cos{\left (x \right )}}{\sqrt{- a^{2} \sin^{2}{\left (x \right )} + 1}} \left(\frac{3 a^{4} \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )}}{\left(- a^{2} \sin^{2}{\left (x \right )} + 1\right)^{2}} - \frac{3 a^{2} \sin^{2}{\left (x \right )}}{- a^{2} \sin^{2}{\left (x \right )} + 1} + \frac{a^{2} \cos^{2}{\left (x \right )}}{- a^{2} \sin^{2}{\left (x \right )} + 1} - 1\right)$$