Производная log(atan(1+x))*l

Вы ввели

log(atan(1 + x))*l

$$l \log{\left (\operatorname{atan}{\left (x + 1 \right )} \right )}$$

Первая производная

            l             
--------------------------
/           2\            
\1 + (1 + x) /*atan(1 + x)

$$\frac{l}{\left(\left(x + 1\right)^{2} + 1\right) \operatorname{atan}{\left (x + 1 \right )}}$$

Вторая производная

   /         1           \ 
-l*|2 + ----------- + 2*x| 
   \    atan(1 + x)      / 
---------------------------
              2            
/           2\             
\1 + (1 + x) / *atan(1 + x)

$$- \frac{l \left(2 x + 2 + \frac{1}{\operatorname{atan}{\left (x + 1 \right )}}\right)}{\left(\left(x + 1\right)^{2} + 1\right)^{2} \operatorname{atan}{\left (x + 1 \right )}}$$

Третья производная

    /                                             2                              \
    |                  1                 4*(1 + x)             3*(1 + x)         |
2*l*|-1 + --------------------------- + ------------ + --------------------------|
    |     /           2\     2                     2   /           2\            |
    \     \1 + (1 + x) /*atan (1 + x)   1 + (1 + x)    \1 + (1 + x) /*atan(1 + x)/
----------------------------------------------------------------------------------
                                         2                                        
                           /           2\                                         
                           \1 + (1 + x) / *atan(1 + x)                            

$$\frac{2 l}{\left(\left(x + 1\right)^{2} + 1\right)^{2} \operatorname{atan}{\left (x + 1 \right )}} \left(\frac{4 \left(x + 1\right)^{2}}{\left(x + 1\right)^{2} + 1} + \frac{3 x + 3}{\left(\left(x + 1\right)^{2} + 1\right) \operatorname{atan}{\left (x + 1 \right )}} - 1 + \frac{1}{\left(\left(x + 1\right)^{2} + 1\right) \operatorname{atan}^{2}{\left (x + 1 \right )}}\right)$$