#include <stdio.h>
#include <math.h>

double f(double x);
double f_prime(double x);


int main () 
{
  int i;                                   
                                   // now define the iteration; start at
                                   // x_0=1
  double x = 10.0;
  printf("x_0 = %.16f \n",x);
  
                                   // do 10 iterations and output the result
  for (i=1; i<=100; i++)
    {
      x = x - f(x)/f_prime(x);
      printf("x_%d = %.16f \n",i,x);
    }
   
  return 0;
}





// define f(x)
double f(double x)
{
  return pow(x,30)-1.;
}


// also define f'(x)
double f_prime (double x)
{
  return 30.*pow(x,29);
}