Производная acot(cos(5*x))

Вы ввели

acot(cos(5*x))

$$\operatorname{acot}{\left (\cos{\left (5 x \right )} \right )}$$

Первая производная

  5*sin(5*x) 
-------------
       2     
1 + cos (5*x)

$$\frac{5 \sin{\left (5 x \right )}}{\cos^{2}{\left (5 x \right )} + 1}$$

Вторая производная

   /          2      \         
   |     2*sin (5*x) |         
25*|1 + -------------|*cos(5*x)
   |           2     |         
   \    1 + cos (5*x)/         
-------------------------------
                2              
         1 + cos (5*x)         

$$\frac{25 \cos{\left (5 x \right )}}{\cos^{2}{\left (5 x \right )} + 1} \left(1 + \frac{2 \sin^{2}{\left (5 x \right )}}{\cos^{2}{\left (5 x \right )} + 1}\right)$$

Третья производная

    /           2               2              2         2     \         
    |      2*sin (5*x)     6*cos (5*x)    8*cos (5*x)*sin (5*x)|         
125*|-1 - ------------- + ------------- + ---------------------|*sin(5*x)
    |            2               2                          2  |         
    |     1 + cos (5*x)   1 + cos (5*x)      /       2     \   |         
    \                                        \1 + cos (5*x)/   /         
-------------------------------------------------------------------------
                                     2                                   
                              1 + cos (5*x)                              

$$\frac{125 \sin{\left (5 x \right )}}{\cos^{2}{\left (5 x \right )} + 1} \left(-1 - \frac{2 \sin^{2}{\left (5 x \right )}}{\cos^{2}{\left (5 x \right )} + 1} + \frac{6 \cos^{2}{\left (5 x \right )}}{\cos^{2}{\left (5 x \right )} + 1} + \frac{8 \sin^{2}{\left (5 x \right )} \cos^{2}{\left (5 x \right )}}{\left(\cos^{2}{\left (5 x \right )} + 1\right)^{2}}\right)$$