Производная log(sinh(x))

Вы ввели

log(sinh(x))

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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