Mathc initiation/a0091

Sommaire

Calculons la dérivée :

         y    = asinh(x)                             *
        
     sinh(y)   = sinh(asinh(x))
    
     sinh(y)   = x    
    
    (sinh(y))' = (x)'  
       

        cosh(y) dy/dx = 1
    
    
               dy/dx =  1/cosh(y) 
                                                    *  y = asinh(x)       
       
       d(asinh(x))/dx =  1/cosh(asinh(x))
                                               ***  cosh(asinh(x)) = sqrt(1+x**2)   ***    
          (asinh(x))' =  1/sqrt(1+x**2)

 *** cosh(asinh(x)) = sqrt(1+x**2) ***