Производная acos(cos(x))

Вы ввели

acos(cos(x))

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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

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