Производная atan(7*x)^5

Вы ввели

    5     
atan (7*x)

$$\operatorname{atan}^{5}{\left(7 x \right)}$$

d /    5     \
--\atan (7*x)/
dx            

$$\frac{d}{d x} \operatorname{atan}^{5}{\left(7 x \right)}$$

Первая производная

       4     
35*atan (7*x)
-------------
          2  
  1 + 49*x   

$$\frac{35 \operatorname{atan}^{4}{\left(7 x \right)}}{49 x^{2} + 1}$$

Вторая производная

        3                         
490*atan (7*x)*(2 - 7*x*atan(7*x))
----------------------------------
                      2           
           /        2\            
           \1 + 49*x /            

$$\frac{490 \left(- 7 x \operatorname{atan}{\left(7 x \right)} + 2\right) \operatorname{atan}^{3}{\left(7 x \right)}}{\left(49 x^{2} + 1\right)^{2}}$$

Третья производная

                /                                                 2     2     \
         2      |      2            6       84*x*atan(7*x)   196*x *atan (7*x)|
3430*atan (7*x)*|- atan (7*x) + --------- - -------------- + -----------------|
                |                       2             2                  2    |
                \               1 + 49*x      1 + 49*x           1 + 49*x     /
-------------------------------------------------------------------------------
                                             2                                 
                                  /        2\                                  
                                  \1 + 49*x /                                  

$$\frac{3430 \cdot \left(\frac{196 x^{2} \operatorname{atan}^{2}{\left(7 x \right)}}{49 x^{2} + 1} - \frac{84 x \operatorname{atan}{\left(7 x \right)}}{49 x^{2} + 1} - \operatorname{atan}^{2}{\left(7 x \right)} + \frac{6}{49 x^{2} + 1}\right) \operatorname{atan}^{2}{\left(7 x \right)}}{\left(49 x^{2} + 1\right)^{2}}$$

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