Производная atan(log(x))^(2)

Вы ввели

    2        
atan (log(x))

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

  /                                                                                                2                \
  |       3                            6*log(x)      2*atan(log(x))   6*atan(log(x))*log(x)   8*log (x)*atan(log(x))|
2*|- ----------- + 2*atan(log(x)) - -------------- - -------------- + --------------------- + ----------------------|
  |         2                                    2           2                    2                            2    |
  |  1 + log (x)                    /       2   \     1 + log (x)          1 + log (x)            /       2   \     |
  \                                 \1 + log (x)/                                                 \1 + log (x)/     /
---------------------------------------------------------------------------------------------------------------------
                                                    3 /       2   \                                                  
                                                   x *\1 + log (x)/                                                  

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