Производная atan(4*x)^(3)

Вы ввели

    3     
atan (4*x)

$$\operatorname{atan}^{3}{\left (4 x \right )}$$

Первая производная

       2     
12*atan (4*x)
-------------
          2  
  1 + 16*x   

$$\frac{12 \operatorname{atan}^{2}{\left (4 x \right )}}{16 x^{2} + 1}$$

Вторая производная

96*(1 - 4*x*atan(4*x))*atan(4*x)
--------------------------------
                     2          
          /        2\           
          \1 + 16*x /           

$$\frac{96 \operatorname{atan}{\left (4 x \right )}}{\left(16 x^{2} + 1\right)^{2}} \left(- 4 x \operatorname{atan}{\left (4 x \right )} + 1\right)$$

Третья производная

    /                                              2     2     \
    |    1           2        24*x*atan(4*x)   64*x *atan (4*x)|
384*|--------- - atan (4*x) - -------------- + ----------------|
    |        2                          2                 2    |
    \1 + 16*x                   1 + 16*x          1 + 16*x     /
----------------------------------------------------------------
                                     2                          
                          /        2\                           
                          \1 + 16*x /                           

$$\frac{1}{\left(16 x^{2} + 1\right)^{2}} \left(\frac{24576 x^{2} \operatorname{atan}^{2}{\left (4 x \right )}}{16 x^{2} + 1} - \frac{9216 x \operatorname{atan}{\left (4 x \right )}}{16 x^{2} + 1} - 384 \operatorname{atan}^{2}{\left (4 x \right )} + \frac{384}{16 x^{2} + 1}\right)$$