Mathc initiation/Fichiers c : c76cq

Sommaire

Installer et compiler ces fichiers dans votre répertoire de travail.

	c01q.c

/* --------------------------------- */
/* save as c1q.c                     */
/* --------------------------------- */
#include "x_hfile.h"
#include      "fq.h"
/* --------------------------------- */
int main(void)
{
double c  = 0.5;

 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-> atanh(x)

 Df : x-> 1/(1-x**2)


  Compute the derivative of f when x = 0.500

  with   Df(0.500) = 1.33333333    
  with fx_x(0.500) = 1.33333335


 Press return to continue.

Calculons la dérivé :

        y = atanh(x)                                        (*)
   
   tanh(y) = tanh(atanh(x))
   
   
   tanh(y) = x                                              (**)
   
   
   (tanh(y))' = (x)'      
   
   sech**2(y) dy/dx = 1
   
                                     
   dy/dx = 1/sech**2(y)               sech**2(x) + tanh**2(x) = 1
                                      sech**2(x) = 1 - tanh**2(x)  

   dy/dx = 1/(1 - tanh**2(y))         
                                         tanh(y) = x          (**)
   dy/dx = 1/(1 - x**2)
   
                                               y = atanh(x)    (*)
   d(atanh(x))/dx = 1/(1 - x**2)    
   
   
      (atanh(x))' = 1/(1 - x**2)