Производная log(atan(x))

Вы ввели

log(atan(x))

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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

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