Производная tan(x)-atan(x)

Вы ввели

tan(x) - atan(x)

$$\tan{\left (x \right )} - \operatorname{atan}{\left (x \right )}$$

Первая производная

       2        1   
1 + tan (x) - ------
                   2
              1 + x 

$$\tan^{2}{\left (x \right )} + 1 - \frac{1}{x^{2} + 1}$$

Вторая производная

  /    x       /       2   \       \
2*|--------- + \1 + tan (x)/*tan(x)|
  |        2                       |
  |/     2\                        |
  \\1 + x /                        /

$$2 \left(\frac{x}{\left(x^{2} + 1\right)^{2}} + \left(\tan^{2}{\left (x \right )} + 1\right) \tan{\left (x \right )}\right)$$

Третья производная

  /                         2         2                            \
  |    1       /       2   \       4*x           2    /       2   \|
2*|--------- + \1 + tan (x)/  - --------- + 2*tan (x)*\1 + tan (x)/|
  |        2                            3                          |
  |/     2\                     /     2\                           |
  \\1 + x /                     \1 + x /                           /

$$2 \left(- \frac{4 x^{2}}{\left(x^{2} + 1\right)^{3}} + \left(\tan^{2}{\left (x \right )} + 1\right)^{2} + 2 \left(\tan^{2}{\left (x \right )} + 1\right) \tan^{2}{\left (x \right )} + \frac{1}{\left(x^{2} + 1\right)^{2}}\right)$$