Производная atan(x)^5

Вы ввели

    5   
atan (x)

$$\operatorname{atan}^{5}{\left (x \right )}$$

Первая производная

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

$$\frac{5 \operatorname{atan}^{4}{\left (x \right )}}{x^{2} + 1}$$

Вторая производная

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

$$\frac{10 \operatorname{atan}^{3}{\left (x \right )}}{\left(x^{2} + 1\right)^{2}} \left(- x \operatorname{atan}{\left (x \right )} + 2\right)$$

Третья производная

            /                                        2     2   \
       2    |      2        6      12*x*atan(x)   4*x *atan (x)|
10*atan (x)*|- atan (x) + ------ - ------------ + -------------|
            |                  2           2               2   |
            \             1 + x       1 + x           1 + x    /
----------------------------------------------------------------
                                   2                            
                           /     2\                             
                           \1 + x /                             

$$\frac{10 \operatorname{atan}^{2}{\left (x \right )}}{\left(x^{2} + 1\right)^{2}} \left(\frac{4 x^{2} \operatorname{atan}^{2}{\left (x \right )}}{x^{2} + 1} - \frac{12 x \operatorname{atan}{\left (x \right )}}{x^{2} + 1} - \operatorname{atan}^{2}{\left (x \right )} + \frac{6}{x^{2} + 1}\right)$$