Производная atan(8*x)^7

Вы ввели

    7     
atan (8*x)

$$\operatorname{atan}^{7}{\left (8 x \right )}$$

Первая производная

       6     
56*atan (8*x)
-------------
          2  
  1 + 64*x   

$$\frac{56 \operatorname{atan}^{6}{\left (8 x \right )}}{64 x^{2} + 1}$$

Вторая производная

        5                         
896*atan (8*x)*(3 - 8*x*atan(8*x))
----------------------------------
                      2           
           /        2\            
           \1 + 64*x /            

$$\frac{896 \operatorname{atan}^{5}{\left (8 x \right )}}{\left(64 x^{2} + 1\right)^{2}} \left(- 8 x \operatorname{atan}{\left (8 x \right )} + 3\right)$$

Третья производная

                /                                                  2     2     \
         4      |      2            15      144*x*atan(8*x)   256*x *atan (8*x)|
7168*atan (8*x)*|- atan (8*x) + --------- - --------------- + -----------------|
                |                       2              2                  2    |
                \               1 + 64*x       1 + 64*x           1 + 64*x     /
--------------------------------------------------------------------------------
                                             2                                  
                                  /        2\                                   
                                  \1 + 64*x /                                   

$$\frac{7168 \operatorname{atan}^{4}{\left (8 x \right )}}{\left(64 x^{2} + 1\right)^{2}} \left(\frac{256 x^{2} \operatorname{atan}^{2}{\left (8 x \right )}}{64 x^{2} + 1} - \frac{144 x \operatorname{atan}{\left (8 x \right )}}{64 x^{2} + 1} - \operatorname{atan}^{2}{\left (8 x \right )} + \frac{15}{64 x^{2} + 1}\right)$$