Производная 1/(2*sinh(x))

Вы ввели

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

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

/          2   \        
|5   3*cosh (x)|        
|- - ----------|*cosh(x)
|2        2    |        
\     sinh (x) /        
------------------------
            2           
        sinh (x)        

$$\frac{\cosh{\left (x \right )}}{\sinh^{2}{\left (x \right )}} \left(\frac{5}{2} - \frac{3 \cosh^{2}{\left (x \right )}}{\sinh^{2}{\left (x \right )}}\right)$$