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)                     

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