Производная acosh(sinh(x))

Вы ввели

acosh(sinh(x))

$$\operatorname{acosh}{\left (\sinh{\left (x \right )} \right )}$$

Первая производная

     cosh(x)      
------------------
   _______________
  /          2    
\/  -1 + sinh (x) 

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

Вторая производная

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

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

Третья производная

/           2                2             2        2   \        
|       cosh (x)       3*sinh (x)    3*cosh (x)*sinh (x)|        
|1 - ------------- - ------------- + -------------------|*cosh(x)
|             2               2                       2 |        
|    -1 + sinh (x)   -1 + sinh (x)     /         2   \  |        
\                                      \-1 + sinh (x)/  /        
-----------------------------------------------------------------
                           _______________                       
                          /          2                           
                        \/  -1 + sinh (x)                        

$$\frac{\cosh{\left (x \right )}}{\sqrt{\sinh^{2}{\left (x \right )} - 1}} \left(1 - \frac{3 \sinh^{2}{\left (x \right )}}{\sinh^{2}{\left (x \right )} - 1} - \frac{\cosh^{2}{\left (x \right )}}{\sinh^{2}{\left (x \right )} - 1} + \frac{3 \sinh^{2}{\left (x \right )} \cosh^{2}{\left (x \right )}}{\left(\sinh^{2}{\left (x \right )} - 1\right)^{2}}\right)$$