Mathc initiation/a0092

Sommaire

Calculons la dérivée :

         y    = acosh(x)                             *
        
     cosh(y)   = cosh(acosh(x))
    
     cosh(y)   = x    
    
    (cosh(y))' = (x)'  
       

       sinh(y) dy/dx = 1
    
    
               dy/dx =  1/sinh(y) 
                                                    *  y = acosh(x)       
       
       d(acosh(x))/dx =  1/sinh(acosh(x))
                                               ***  sinh(acosh(x)) = sqrt(x**2-1)   ***    
          (acosh(x))' =  1/sqrt(x**2-1)

 *** sinh(acosh(x)) = sqrt(x**2-1)) ***