Производная atan(log(5*x))

Вы ввели

atan(log(5*x))

$$\operatorname{atan}{\left (\log{\left (5 x \right )} \right )}$$

Первая производная

        1        
-----------------
  /       2     \
x*\1 + log (5*x)/

$$\frac{1}{x \left(\log^{2}{\left (5 x \right )} + 1\right)}$$

Вторая производная

 /      2*log(5*x) \ 
-|1 + -------------| 
 |           2     | 
 \    1 + log (5*x)/ 
---------------------
   2 /       2     \ 
  x *\1 + log (5*x)/ 

$$- \frac{1 + \frac{2 \log{\left (5 x \right )}}{\log^{2}{\left (5 x \right )} + 1}}{x^{2} \left(\log^{2}{\left (5 x \right )} + 1\right)}$$

Третья производная

  /                                           2        \
  |          1           3*log(5*x)      4*log (5*x)   |
2*|1 - ------------- + ------------- + ----------------|
  |           2               2                       2|
  |    1 + log (5*x)   1 + log (5*x)   /       2     \ |
  \                                    \1 + log (5*x)/ /
--------------------------------------------------------
                    3 /       2     \                   
                   x *\1 + log (5*x)/                   

$$\frac{1}{x^{3} \left(\log^{2}{\left (5 x \right )} + 1\right)} \left(2 + \frac{6 \log{\left (5 x \right )}}{\log^{2}{\left (5 x \right )} + 1} - \frac{2}{\log^{2}{\left (5 x \right )} + 1} + \frac{8 \log^{2}{\left (5 x \right )}}{\left(\log^{2}{\left (5 x \right )} + 1\right)^{2}}\right)$$