Производная atanh(log(x))

Вы ввели

atanh(log(x))

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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