Производная (acos(sin(x)))^3

Вы ввели

    3        
acos (sin(x))

$$\operatorname{acos}^{3}{\left (\sin{\left (x \right )} \right )}$$

Первая производная

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

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

Вторая производная

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

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

Третья производная

  /     2                     2              2            2            2            2                                    2            2       2           2                       \       
  | acos (sin(x))        2*cos (x)       acos (sin(x))*cos (x)   3*acos (sin(x))*sin (x)   6*acos(sin(x))*sin(x)   3*acos (sin(x))*cos (x)*sin (x)   6*cos (x)*acos(sin(x))*sin(x)|       
3*|---------------- - ---------------- - --------------------- + ----------------------- + --------------------- - ------------------------------- + -----------------------------|*cos(x)
  |   _____________                3/2                   3/2                      3/2                   2                               5/2                               2       |       
  |  /        2       /       2   \         /       2   \            /       2   \              -1 + sin (x)               /       2   \                    /        2   \        |       
  \\/  1 - sin (x)    \1 - sin (x)/         \1 - sin (x)/            \1 - sin (x)/                                         \1 - sin (x)/                    \-1 + sin (x)/        /       

$$3 \left(\frac{6 \sin{\left (x \right )} \operatorname{acos}{\left (\sin{\left (x \right )} \right )}}{\sin^{2}{\left (x \right )} - 1} + \frac{6 \cos^{2}{\left (x \right )} \operatorname{acos}{\left (\sin{\left (x \right )} \right )}}{\left(\sin^{2}{\left (x \right )} - 1\right)^{2}} \sin{\left (x \right )} + \frac{\operatorname{acos}^{2}{\left (\sin{\left (x \right )} \right )}}{\sqrt{- \sin^{2}{\left (x \right )} + 1}} + \frac{3 \sin^{2}{\left (x \right )} \operatorname{acos}^{2}{\left (\sin{\left (x \right )} \right )}}{\left(- \sin^{2}{\left (x \right )} + 1\right)^{\frac{3}{2}}} - \frac{\cos^{2}{\left (x \right )} \operatorname{acos}^{2}{\left (\sin{\left (x \right )} \right )}}{\left(- \sin^{2}{\left (x \right )} + 1\right)^{\frac{3}{2}}} - \frac{2 \cos^{2}{\left (x \right )}}{\left(- \sin^{2}{\left (x \right )} + 1\right)^{\frac{3}{2}}} - \frac{3 \cos^{2}{\left (x \right )} \operatorname{acos}^{2}{\left (\sin{\left (x \right )} \right )}}{\left(- \sin^{2}{\left (x \right )} + 1\right)^{\frac{5}{2}}} \sin^{2}{\left (x \right )}\right) \cos{\left (x \right )}$$