Производная atan(x)^4

Вы ввели

    4   
atan (x)

$$\operatorname{atan}^{4}{\left (x \right )}$$

Первая производная

      3   
4*atan (x)
----------
       2  
  1 + x   

$$\frac{4 \operatorname{atan}^{3}{\left (x \right )}}{x^{2} + 1}$$

Вторая производная

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

$$\frac{4 \operatorname{atan}^{2}{\left (x \right )}}{\left(x^{2} + 1\right)^{2}} \left(- 2 x \operatorname{atan}{\left (x \right )} + 3\right)$$

Третья производная

  /                                       2     2   \        
  |      2        3      9*x*atan(x)   4*x *atan (x)|        
8*|- atan (x) + ------ - ----------- + -------------|*atan(x)
  |                  2           2              2   |        
  \             1 + x       1 + x          1 + x    /        
-------------------------------------------------------------
                                  2                          
                          /     2\                           
                          \1 + x /                           

$$\frac{8 \operatorname{atan}{\left (x \right )}}{\left(x^{2} + 1\right)^{2}} \left(\frac{4 x^{2} \operatorname{atan}^{2}{\left (x \right )}}{x^{2} + 1} - \frac{9 x \operatorname{atan}{\left (x \right )}}{x^{2} + 1} - \operatorname{atan}^{2}{\left (x \right )} + \frac{3}{x^{2} + 1}\right)$$