Производная 1/acot(x)

Вы ввели

   1   
-------
acot(x)

$$\frac{1}{\operatorname{acot}{\left (x \right )}}$$

Первая производная

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

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

Вторая производная

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

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

Третья производная

  /                             2                    \
  |             3            4*x           6*x       |
2*|-1 + ----------------- + ------ - ----------------|
  |     /     2\     2           2   /     2\        |
  \     \1 + x /*acot (x)   1 + x    \1 + x /*acot(x)/
------------------------------------------------------
                          2                           
                  /     2\      2                     
                  \1 + x / *acot (x)                  

$$\frac{1}{\left(x^{2} + 1\right)^{2} \operatorname{acot}^{2}{\left (x \right )}} \left(\frac{8 x^{2}}{x^{2} + 1} - \frac{12 x}{\left(x^{2} + 1\right) \operatorname{acot}{\left (x \right )}} - 2 + \frac{6}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left (x \right )}}\right)$$