Mathc initiation/a0079

Sommaire

Calculons la dérivée :

         y    = asin(x)                             *  y = asin(x)
        
     sin(y)   = sin(asin(x))
    
     sin(y)   = x    
    
    (sin(y))' = (x)'  
       

        cos(y) dy/dx = 1
    
    
               dy/dx =  1/cos(y) 
                                                    *  y = asin(x)       
       
       d(asin(x))/dx =  1/cos(asin(x))
                                               *** cos(asin(x)) = sqrt(1-x**2) ***    
          (asin(x))' =  1/sqrt(1-x**2)

 *** cos(asin(x)) = sqrt(1-x**2) ***