Производная cos(x)*acot(x)

Вы ввели

cos(x)*acot(x)

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

                                           2                    
                  2*cos(x)   3*cos(x)   8*x *cos(x)   6*x*sin(x)
acot(x)*sin(x) + --------- + -------- - ----------- - ----------
                         2         2             3            2 
                 /     2\     1 + x      /     2\     /     2\  
                 \1 + x /                \1 + x /     \1 + x /  

$$- \frac{8 x^{2} \cos{\left (x \right )}}{\left(x^{2} + 1\right)^{3}} - \frac{6 x \sin{\left (x \right )}}{\left(x^{2} + 1\right)^{2}} + \sin{\left (x \right )} \operatorname{acot}{\left (x \right )} + \frac{3 \cos{\left (x \right )}}{x^{2} + 1} + \frac{2 \cos{\left (x \right )}}{\left(x^{2} + 1\right)^{2}}$$