Производная atan(log(a*x+b))

Вы ввели

atan(log(a*x + b))

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

$$\frac{2 a^{3}}{\left(a x + b\right)^{3} \left(\log^{2}{\left (a x + b \right )} + 1\right)} \left(1 + \frac{3 \log{\left (a x + b \right )}}{\log^{2}{\left (a x + b \right )} + 1} - \frac{1}{\log^{2}{\left (a x + b \right )} + 1} + \frac{4 \log^{2}{\left (a x + b \right )}}{\left(\log^{2}{\left (a x + b \right )} + 1\right)^{2}}\right)$$