#include<iostream>
#include<iomanip>
#include<math.h>
using namespace std;

/* Calcul de la derivee d'une fonction */

double f(double x){
  return atan(x);
}

double f2(double x){
  return x*(x-1)*(x-2);
}

double derivee(double (*g)(double), double x0, double Dx){
  double res;

  res = (*g)(x0-2.*Dx) - 8.*(*g)(x0-Dx) + 8.*(*g)(x0+Dx) - (*g)(x0+2.*Dx);
  return res/(12.*Dx);
}

int main(){
  double x0 = 2.;
  double Dx = 2.;
  int i;

  cout << setprecision(15);
  cout << "Arctan'(" << x0 << ")" << endl;
  for (i = 0; i < 10; i++){
    cout << Dx << " : " << derivee(f,x0,Dx) << endl;
    Dx = Dx/2.;
  }
  cout << "Exact : " << 1./(1.+x0*x0) << endl << endl;
  Dx = 2.;
  cout << "[x(x-2)(x-1)]'(" << x0 << ")" << endl;
  for (i = 0; i < 10; i++){
    cout << Dx << " : " << derivee(f2,x0,Dx) << endl;
    Dx = Dx/2.;
  }
  cout << "Exact : " << 3.*x0*x0-6.*x0+2. << endl;
  return 0;
}