Mathc initiation/Fichiers c : c76cu

Sommaire

Installer et compiler ces fichiers dans votre répertoire de travail.

	c01t.c

/* --------------------------------- */
/* save as c1u.c                     */
/* --------------------------------- */
#include "x_hfile.h"
#include      "fu.h"
/* --------------------------------- */
int main(void)
{
double c  =  .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-> asech(x)

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


  Compute the derivative of f when x = 0.500

  with   Df(0.500) = -2.30940108    
  with fx_x(0.500) = -2.30940111


 Press return to continue.

Calculons la dérivé :

          y    = asech(x)                             *
        
     sech(y)   = sech(asech(x))
    
     sech(y)   = x    
    
    (sech(y))' = (x)'  
       

      - sech(y) tanh(y)  dy/dx = 1
    
    
               dy/dx =  1/(- sech(y) tanh(y)) 
            
               dy/dx = -1/(  sech(y) tanh(y))       
                                                    *  y = asech(x)  
                                                                                                               
       d(asech(x))/dx = -1/(  sech(asech(x)) tanh(asech(x)))
       
       d(asech(x))/dx = -1/(             x   tanh(asech(x)))
              
                                               ***  tanh(asech(x)) = sqrt(1-x**2)   ***  
                                               
       d(asech(x))/dx = -1/(             x   sqrt(1-x**2))                                               
                                                 
          (asech(x))' =  -1/(x sqrt(1-x**2))

 *** tanh(asech(x)) = sqrt(1-x**2) ***