Производная atan(cos(x))

Вы ввели

atan(cos(x))

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

Первая производная

  -sin(x)  
-----------
       2   
1 + cos (x)

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

Вторая производная

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

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

Третья производная

/          2             2            2       2   \       
|     6*cos (x)     2*sin (x)    8*cos (x)*sin (x)|       
|1 - ----------- + ----------- - -----------------|*sin(x)
|           2             2                     2 |       
|    1 + cos (x)   1 + cos (x)     /       2   \  |       
\                                  \1 + cos (x)/  /       
----------------------------------------------------------
                              2                           
                       1 + cos (x)                        

$$\frac{\sin{\left (x \right )}}{\cos^{2}{\left (x \right )} + 1} \left(1 + \frac{2 \sin^{2}{\left (x \right )}}{\cos^{2}{\left (x \right )} + 1} - \frac{6 \cos^{2}{\left (x \right )}}{\cos^{2}{\left (x \right )} + 1} - \frac{8 \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )}}{\left(\cos^{2}{\left (x \right )} + 1\right)^{2}}\right)$$