Производная log(atan(1+x))

Вы ввели

log(atan(1 + x))

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

$$\frac{1}{\left(\left(x + 1\right)^{2} + 1\right)^{2} \operatorname{atan}{\left (x + 1 \right )}} \left(\frac{8 \left(x + 1\right)^{2}}{\left(x + 1\right)^{2} + 1} + \frac{6 x + 6}{\left(\left(x + 1\right)^{2} + 1\right) \operatorname{atan}{\left (x + 1 \right )}} - 2 + \frac{2}{\left(\left(x + 1\right)^{2} + 1\right) \operatorname{atan}^{2}{\left (x + 1 \right )}}\right)$$