/* calculation of derivative central method*/
#include <iostream>
#include <iomanip>
#include <cmath>
using namespace std;

double f(double x) { return x*x+exp(x)+log(x)+sin(x); }
double fp(double x){ return 2.*x+exp(x)+1./x+cos(x); }

int main()
{
	double x = 0.5;
	double h = 1E-2;
	double fp_exact = fp(x);

	cout << "Exacto: " << setprecision(18) << fp_exact << endl;
	cout << "   h \t Valor aprox.  \t\t diferencia" << endl;
	while(h>1E-15) {
        double fp_numeric = (f(x+h/2.) - f(x-h/2.))/h;
	    cout << setprecision(8) << h << "\t" << setprecision(18) << fp_numeric << " \t" << fabs(fp_numeric-fp_exact) << endl;
		h /= 10.;
	}
}