Производная atan(log(x))

Вы ввели

atan(log(x))

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

$$\frac{1}{x^{3} \left(\log^{2}{\left (x \right )} + 1\right)} \left(2 + \frac{6 \log{\left (x \right )}}{\log^{2}{\left (x \right )} + 1} - \frac{2}{\log^{2}{\left (x \right )} + 1} + \frac{8 \log^{2}{\left (x \right )}}{\left(\log^{2}{\left (x \right )} + 1\right)^{2}}\right)$$