Производная atan((log(x))/3)

Вы ввели

    /log(x)\
atan|------|
    \  3   /

$$\operatorname{atan}{\left (\frac{1}{3} \log{\left (x \right )} \right )}$$

Первая производная

        1        
-----------------
    /       2   \
    |    log (x)|
3*x*|1 + -------|
    \       9   /

$$\frac{1}{3 x \left(\frac{1}{9} \log^{2}{\left (x \right )} + 1\right)}$$

Вторая производная

   /      2*log(x) \
-3*|1 + -----------|
   |           2   |
   \    9 + log (x)/
--------------------
   2 /       2   \  
  x *\9 + log (x)/  

$$- \frac{3 + \frac{6 \log{\left (x \right )}}{\log^{2}{\left (x \right )} + 9}}{x^{2} \left(\log^{2}{\left (x \right )} + 9\right)}$$

Третья производная

  /                                       2      \
  |         1          3*log(x)      4*log (x)   |
6*|1 - ----------- + ----------- + --------------|
  |           2             2                   2|
  |    9 + log (x)   9 + log (x)   /       2   \ |
  \                                \9 + log (x)/ /
--------------------------------------------------
                  3 /       2   \                 
                 x *\9 + log (x)/                 

$$\frac{1}{x^{3} \left(\log^{2}{\left (x \right )} + 9\right)} \left(6 + \frac{18 \log{\left (x \right )}}{\log^{2}{\left (x \right )} + 9} - \frac{6}{\log^{2}{\left (x \right )} + 9} + \frac{24 \log^{2}{\left (x \right )}}{\left(\log^{2}{\left (x \right )} + 9\right)^{2}}\right)$$