Производная acos((cos(x))^2)

Вы ввели

    /   2   \
acos\cos (x)/

$$\operatorname{acos}{\left (\cos^{2}{\left (x \right )} \right )}$$

Первая производная

2*cos(x)*sin(x) 
----------------
   _____________
  /        4    
\/  1 - cos (x) 

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

Вторая производная

  /                         4       2   \
  |   2         2      2*cos (x)*sin (x)|
2*|cos (x) - sin (x) - -----------------|
  |                              4      |
  \                       1 - cos (x)   /
-----------------------------------------
                _____________            
               /        4                
             \/  1 - cos (x)             

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

Третья производная

  /           4            2       2           6       2   \              
  |      3*cos (x)    5*cos (x)*sin (x)   6*cos (x)*sin (x)|              
4*|-2 - ----------- + ----------------- + -----------------|*cos(x)*sin(x)
  |            4                4                        2 |              
  |     1 - cos (x)      1 - cos (x)        /       4   \  |              
  \                                         \1 - cos (x)/  /              
--------------------------------------------------------------------------
                                _____________                             
                               /        4                                 
                             \/  1 - cos (x)                              

$$\frac{4 \sin{\left (x \right )} \cos{\left (x \right )}}{\sqrt{- \cos^{4}{\left (x \right )} + 1}} \left(-2 + \frac{5 \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )}}{- \cos^{4}{\left (x \right )} + 1} - \frac{3 \cos^{4}{\left (x \right )}}{- \cos^{4}{\left (x \right )} + 1} + \frac{6 \sin^{2}{\left (x \right )} \cos^{6}{\left (x \right )}}{\left(- \cos^{4}{\left (x \right )} + 1\right)^{2}}\right)$$