Производная asin(x)*sin(x)

Вы ввели

asin(x)*sin(x)

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

Первая производная

   sin(x)                   
----------- + asin(x)*cos(x)
   ________                 
  /      2                  
\/  1 - x                   

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

Вторая производная

                    2*cos(x)      x*sin(x) 
-asin(x)*sin(x) + ----------- + -----------
                     ________           3/2
                    /      2    /     2\   
                  \/  1 - x     \1 - x /   

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

Третья производная

                                                              2       
   sin(x)                        3*sin(x)     3*x*cos(x)   3*x *sin(x)
----------- - asin(x)*cos(x) - ----------- + ----------- + -----------
        3/2                       ________           3/2           5/2
/     2\                         /      2    /     2\      /     2\   
\1 - x /                       \/  1 - x     \1 - x /      \1 - x /   

$$\frac{3 x^{2} \sin{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} + \frac{3 x \cos{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} - \cos{\left (x \right )} \operatorname{asin}{\left (x \right )} - \frac{3 \sin{\left (x \right )}}{\sqrt{- x^{2} + 1}} + \frac{\sin{\left (x \right )}}{\left(- x^{2} + 1\right)^{\frac{3}{2}}}$$