Производная log(atan(x)^(2))

Вы ввели

   /    2   \
log\atan (x)/

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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