Производная log(acot(x))

Вы ввели

log(acot(x))

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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