Производная log(cosh(x))

Вы ввели

log(cosh(x))

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

Первая производная

sinh(x)
-------
cosh(x)

$$\frac{\sinh{\left (x \right )}}{\cosh{\left (x \right )}}$$

Вторая производная

        2   
    sinh (x)
1 - --------
        2   
    cosh (x)

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

Третья производная

  /         2   \        
  |     sinh (x)|        
2*|-1 + --------|*sinh(x)
  |         2   |        
  \     cosh (x)/        
-------------------------
         cosh(x)         

$$\frac{2 \sinh{\left (x \right )}}{\cosh{\left (x \right )}} \left(\frac{\sinh^{2}{\left (x \right )}}{\cosh^{2}{\left (x \right )}} - 1\right)$$