Производная log(x)*acot(x)

Вы ввели

log(x)*acot(x)

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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