Производная 1/sinh(x)

Вы ввели

   1   
-------
sinh(x)

$$\frac{1}{\sinh{\left (x \right )}}$$

Первая производная

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

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

Вторая производная

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

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

Третья производная

/          2   \        
|    6*cosh (x)|        
|5 - ----------|*cosh(x)
|         2    |        
\     sinh (x) /        
------------------------
            2           
        sinh (x)        

$$\frac{\cosh{\left (x \right )}}{\sinh^{2}{\left (x \right )}} \left(5 - \frac{6 \cosh^{2}{\left (x \right )}}{\sinh^{2}{\left (x \right )}}\right)$$