Производная atan(log(5*x-3))

Вы ввели

atan(log(5*x - 3))

$$\operatorname{atan}{\left (\log{\left (5 x - 3 \right )} \right )}$$

Первая производная

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

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

Вторая производная

      /     2*log(-3 + 5*x)  \  
  -25*|1 + ------------------|  
      |           2          |  
      \    1 + log (-3 + 5*x)/  
--------------------------------
/       2          \           2
\1 + log (-3 + 5*x)/*(-3 + 5*x) 

$$- \frac{25 + \frac{50 \log{\left (5 x - 3 \right )}}{\log^{2}{\left (5 x - 3 \right )} + 1}}{\left(5 x - 3\right)^{2} \left(\log^{2}{\left (5 x - 3 \right )} + 1\right)}$$

Третья производная

    /                                                      2            \
    |            1             3*log(-3 + 5*x)        4*log (-3 + 5*x)  |
250*|1 - ------------------ + ------------------ + ---------------------|
    |           2                    2                                 2|
    |    1 + log (-3 + 5*x)   1 + log (-3 + 5*x)   /       2          \ |
    \                                              \1 + log (-3 + 5*x)/ /
-------------------------------------------------------------------------
                     /       2          \           3                    
                     \1 + log (-3 + 5*x)/*(-3 + 5*x)                     

$$\frac{1}{\left(5 x - 3\right)^{3} \left(\log^{2}{\left (5 x - 3 \right )} + 1\right)} \left(250 + \frac{750 \log{\left (5 x - 3 \right )}}{\log^{2}{\left (5 x - 3 \right )} + 1} - \frac{250}{\log^{2}{\left (5 x - 3 \right )} + 1} + \frac{1000 \log^{2}{\left (5 x - 3 \right )}}{\left(\log^{2}{\left (5 x - 3 \right )} + 1\right)^{2}}\right)$$