Mathc initiation/Fichiers c : c76cp

Sommaire

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	c01p.c

/* --------------------------------- */
/* save as c1p.c                     */
/* --------------------------------- */
#include "x_hfile.h"
#include      "fp.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-> acsc(x)

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


  Compute the derivative of f when x = 1.500

  with   Df(1.500) = -0.59628479    
  with fx_x(1.500) = -0.59628480


 Press return to continue.

Calculons la dérivé :

         y    = acsc(x)                             *
        
     csc(y)   = csc(acsc(x))
    
     csc(y)   = x                                   *
    
    (csc(y))' = (x)'  
       

 (-csc(y) cot(y)) dy/dx = 1

    
                 dy/dx =  1/(-csc(y) cot(y)) 
                       = -1/( csc(y) cot(y)) 
                                                    * csc(y) = x
                                                    *     y  = acsc(x)     
       
       d(acsc(x))/dx =  -1/(x cot(acsc(x))) 
                                               *** cot(acsc(x)) = sqrt(x**2-1) ***    
          (acsc(x))' =  -1/(x sqrt(x**2-1))

 *** cot(acsc(x)) = sqrt(x**2-1) ***