Производная 1/cosh(x)

Вы ввели

   1   
-------
cosh(x)

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

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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

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