Производная 3/acot(x)^(3)

Вы ввели

   3    
--------
    3   
acot (x)

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

Первая производная

        9        
-----------------
/     2\     4   
\1 + x /*acot (x)

$$\frac{9}{\left(x^{2} + 1\right) \operatorname{acot}^{4}{\left (x \right )}}$$

Вторая производная

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

$$\frac{- 18 x + \frac{36}{\operatorname{acot}{\left (x \right )}}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}^{4}{\left (x \right )}}$$

Третья производная

   /         2                                        \
   |      4*x             10                12*x      |
18*|-1 + ------ + ----------------- - ----------------|
   |          2   /     2\     2      /     2\        |
   \     1 + x    \1 + x /*acot (x)   \1 + x /*acot(x)/
-------------------------------------------------------
                           2                           
                   /     2\      4                     
                   \1 + x / *acot (x)                  

$$\frac{1}{\left(x^{2} + 1\right)^{2} \operatorname{acot}^{4}{\left (x \right )}} \left(\frac{72 x^{2}}{x^{2} + 1} - \frac{216 x}{\left(x^{2} + 1\right) \operatorname{acot}{\left (x \right )}} - 18 + \frac{180}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left (x \right )}}\right)$$