Mathc initiation/Fichiers c : c76cr

Sommaire

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	c01r.c

/* --------------------------------- */
/* save as c1r.c                     */
/* --------------------------------- */
#include "x_hfile.h"
#include      "fr.h"
/* --------------------------------- */
int main(void)
{
double c  = 1.5;

 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-> acoth(x)

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


  Compute the derivative of f when x = 1.500

  with   Df(1.500) = -0.80000000    
  with fx_x(1.500) = -0.80000001


 Press return to continue.

Calculons la dérivé :

        y = acoth(x)                                        (*)
   
   coth(y) = coth(acoth(x))
   
   
   coth(y) = x                                              (**)
   
   
   (coth(y))' = (x)'      
   
   -csch**2(y) dy/dx = 1
   
                                     
   dy/dx =  1/(-csch**2(y))
   
   dy/dx = -1/  csch**2(y)             coth**2(x) - csch**2(x) =  1
                                                  - csch**2(x) =  1 -coth**2(x) 
                                                    csch**2(x) = -1 +coth**2(x)   
                                                    csch**2(x) = coth**2(x) - 1 
   dy/dx = -1/(coth**2(y) - 1)         
                                         coth(y) = x          (**)
   dy/dx = -1/(x**2 - 1)
   
                                               y = acoth(x)    (*)
   d(acoth(x))/dx = -1/(x**2 - 1)   
   
   
      (acoth(x))' = -1/(x**2 - 1)
      
      (acoth(x))' =  1/(1 - x**2)