Mathc initiation/a19

Sommaire

Installer et compiler ces fichiers dans votre répertoire de travail.

	c01a.c

/* --------------------------------- */
/* save as c1a.c                     */
/* --------------------------------- */
#include "x_hfile.h"
#include      "fa.h"
/* --------------------------------- */
int main(void)
{
double c  = 1;

 clrscrn();
 printf("  f : x-> %s\n\n" 
        " Df : x-> %s\n\n\n", feq, Dfeq);

 printf("  Compute the derivative of f when x = %0.3f\n\n", c);   
  
 printf("  with   Df(%0.3f) = %0.8f    \n",c, Df(c));
 printf("  with fx_x(%0.3f) = %0.8f\n\n\n",c, fx_x(f,c,H));
 stop();

 return 0;
}
/* ---------------------------------- */
/* ---------------------------------- */

Calculons la dérivé de la fonction f :

Exemple de sortie écran :

  f : x-> cos(x)

 Df : x-> -sin(x)


  Compute the derivative of f when x = 1.000

  with   Df(1.000) = -0.84147098    
  with fx_x(1.000) = -0.84147098


 Press return to continue.

Calculons la dérivé :

                  cos(x+h) - cos(x)
  cos(x)' = lim   -----------------  
            h->0           h
       
       
                 (cos(x)cos(h)- sin(x)sin(h)) - cos(x)
 cos(x)' = lim    ------------------------------------  
           h->0                  h       


                 (cos(x)cos(h) - cos(x)) - sin(x)sin(h)
 cos(x)' = lim    --------------------------------------  
           h->0                  h       


                  cos(x) (cos(h)-1)            sin(x)sin(h)
 cos(x)' = lim    ----------------- -    lim   ------------  
           h->0         h                h->0     h
       
       
                          (cos(h)-1)                   sin(h)
 cos(x)' =   cos(x) lim   ----------  -  sin(x)  lim   ------ 
                    h->0      h                  h->0    h

                        
 cos(x)' =   cos(x) 0 - sin(x) 1  
                                  


 cos(x)' =  -sin(x)