Производная log(x)*atan(x)

Вы ввели

log(x)*atan(x)

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

Первая производная

atan(x)   log(x)
------- + ------
   x           2
          1 + x 

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

Вторая производная

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

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

Третья производная

                                                       2       
      6            3         2*log(x)   2*atan(x)   8*x *log(x)
- --------- - ----------- - --------- + --------- + -----------
          2    2 /     2\           2        3               3 
  /     2\    x *\1 + x /   /     2\        x        /     2\  
  \1 + x /                  \1 + x /                 \1 + x /  

$$\frac{8 x^{2} \log{\left (x \right )}}{\left(x^{2} + 1\right)^{3}} - \frac{2 \log{\left (x \right )}}{\left(x^{2} + 1\right)^{2}} - \frac{6}{\left(x^{2} + 1\right)^{2}} - \frac{3}{x^{2} \left(x^{2} + 1\right)} + \frac{2}{x^{3}} \operatorname{atan}{\left (x \right )}$$