Производная log(acot(x)^2)

Вы ввели

   /    2   \
log\acot (x)/

$$\log{\left (\operatorname{acot}^{2}{\left (x \right )} \right )}$$

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

$$\frac{1}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left (x \right )}} \left(- \frac{16 x^{2}}{x^{2} + 1} + \frac{12 x}{\left(x^{2} + 1\right) \operatorname{acot}{\left (x \right )}} + 4 - \frac{4}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left (x \right )}}\right)$$