Производная 7*atan(x)^(3)

Вы ввели

      3   
7*atan (x)

$$7 \operatorname{atan}^{3}{\left (x \right )}$$

Первая производная

       2   
21*atan (x)
-----------
        2  
   1 + x   

$$\frac{21 \operatorname{atan}^{2}{\left (x \right )}}{x^{2} + 1}$$

Вторая производная

42*(1 - x*atan(x))*atan(x)
--------------------------
                2         
        /     2\          
        \1 + x /          

$$\frac{42 \operatorname{atan}{\left (x \right )}}{\left(x^{2} + 1\right)^{2}} \left(- x \operatorname{atan}{\left (x \right )} + 1\right)$$

Третья производная

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

$$\frac{1}{\left(x^{2} + 1\right)^{2}} \left(\frac{168 x^{2} \operatorname{atan}^{2}{\left (x \right )}}{x^{2} + 1} - \frac{252 x \operatorname{atan}{\left (x \right )}}{x^{2} + 1} - 42 \operatorname{atan}^{2}{\left (x \right )} + \frac{42}{x^{2} + 1}\right)$$