Mathc initiation/a21

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-> sin(x)

 Df : x-> cos(x)


  Compute the derivative of f when x = 1.000

  with   Df(1.000) = 0.54030231    
  with fx_x(1.000) = 0.54030230


 Press return to continue.

Calculons la dérivé :

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


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


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

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

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


 sin(x)' =  cos(x)