Производная acot(x)^3

Вы ввели

    3   
acot (x)

$$\operatorname{acot}^{3}{\left (x \right )}$$

Первая производная

       2   
-3*acot (x)
-----------
        2  
   1 + x   

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

Вторая производная

6*(1 + x*acot(x))*acot(x)
-------------------------
                2        
        /     2\         
        \1 + x /         

$$\frac{6 \operatorname{acot}{\left (x \right )}}{\left(x^{2} + 1\right)^{2}} \left(x \operatorname{acot}{\left (x \right )} + 1\right)$$

Третья производная

  /                                     2     2   \
  |    2        1      6*x*acot(x)   4*x *acot (x)|
6*|acot (x) - ------ - ----------- - -------------|
  |                2           2              2   |
  \           1 + x       1 + x          1 + x    /
---------------------------------------------------
                             2                     
                     /     2\                      
                     \1 + x /                      

$$\frac{1}{\left(x^{2} + 1\right)^{2}} \left(- \frac{24 x^{2} \operatorname{acot}^{2}{\left (x \right )}}{x^{2} + 1} - \frac{36 x \operatorname{acot}{\left (x \right )}}{x^{2} + 1} + 6 \operatorname{acot}^{2}{\left (x \right )} - \frac{6}{x^{2} + 1}\right)$$