Mathc initiation/a0083

Sommaire

Calculons la dérivée :

         y    = asec(x)                             *
        
     sec(y)   = sec(asec(x))
    
     sec(y)   = x                                   *
    
    (sec(y))' = (x)'  
       

   sec(y) tan(y) dy/dx = 1

    
                 dy/dx =  1/(sec(y) tan(y)) 
                                                    * sec(y) = x
                                                    *     y  = asec(x)     
       
       d(asec(x))/dx =  1/(x tan(asec(x))) 
                                               *** tan(asec(x)) = sqrt(x**2-1) ***    
          (asec(x))' =  1/(x sqrt(x**2-1))

 *** tan(asec(x)) = sqrt(x**2-1) ***