Производная cbrt(atan(x))

Вы ввели

3 _________
\/ atan(x) 

$$\sqrt[3]{\operatorname{atan}{\left (x \right )}}$$

Первая производная

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

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

Вторая производная

     /   1         \  
  -2*|------- + 3*x|  
     \atan(x)      /  
----------------------
          2           
  /     2\      2/3   
9*\1 + x / *atan   (x)

$$- \frac{6 x + \frac{2}{\operatorname{atan}{\left (x \right )}}}{9 \left(x^{2} + 1\right)^{2} \operatorname{atan}^{\frac{2}{3}}{\left (x \right )}}$$

Третья производная

  /                             2                    \
  |             5           36*x           18*x      |
2*|-9 + ----------------- + ------ + ----------------|
  |     /     2\     2           2   /     2\        |
  \     \1 + x /*atan (x)   1 + x    \1 + x /*atan(x)/
------------------------------------------------------
                          2                           
                  /     2\      2/3                   
               27*\1 + x / *atan   (x)                

$$\frac{1}{27 \left(x^{2} + 1\right)^{2} \operatorname{atan}^{\frac{2}{3}}{\left (x \right )}} \left(\frac{72 x^{2}}{x^{2} + 1} + \frac{36 x}{\left(x^{2} + 1\right) \operatorname{atan}{\left (x \right )}} - 18 + \frac{10}{\left(x^{2} + 1\right) \operatorname{atan}^{2}{\left (x \right )}}\right)$$

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