Производная log(atan(x^2))

Вы ввели

   /    / 2\\
log\atan\x //

$$\log{\left (\operatorname{atan}{\left (x^{2} \right )} \right )}$$

Первая производная

       2*x       
-----------------
/     4\     / 2\
\1 + x /*atan\x /

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

Вторая производная

  /        4              2      \
  |     4*x            2*x       |
2*|1 - ------ - -----------------|
  |         4   /     4\     / 2\|
  \    1 + x    \1 + x /*atan\x //
----------------------------------
        /     4\     / 2\         
        \1 + x /*atan\x /         

$$\frac{1}{\left(x^{4} + 1\right) \operatorname{atan}{\left (x^{2} \right )}} \left(- \frac{8 x^{4}}{x^{4} + 1} - \frac{4 x^{2}}{\left(x^{4} + 1\right) \operatorname{atan}{\left (x^{2} \right )}} + 2\right)$$

Третья производная

    /                         6              2                    4      \
    |      2      3       16*x            4*x                 12*x       |
4*x*|- 10*x  - -------- + ------ + ------------------ + -----------------|
    |              / 2\        4   /     4\     2/ 2\   /     4\     / 2\|
    \          atan\x /   1 + x    \1 + x /*atan \x /   \1 + x /*atan\x //
--------------------------------------------------------------------------
                                    2                                     
                            /     4\      / 2\                            
                            \1 + x / *atan\x /                            

$$\frac{4 x}{\left(x^{4} + 1\right)^{2} \operatorname{atan}{\left (x^{2} \right )}} \left(\frac{16 x^{6}}{x^{4} + 1} + \frac{12 x^{4}}{\left(x^{4} + 1\right) \operatorname{atan}{\left (x^{2} \right )}} - 10 x^{2} + \frac{4 x^{2}}{\left(x^{4} + 1\right) \operatorname{atan}^{2}{\left (x^{2} \right )}} - \frac{3}{\operatorname{atan}{\left (x^{2} \right )}}\right)$$