Производная log(tanh(x))

Вы ввели

log(tanh(x))

$$\log{\left (\tanh{\left (x \right )} \right )}$$

Первая производная

        2   
1 - tanh (x)
------------
  tanh(x)   

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

Вторая производная

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

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

Третья производная

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

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