Untitled

#include <stdio.h>

// Function to calculate the derivative using Newton divided difference
double newtonDividedDifference(double x[], double y[], int n, double target) {
    double result = 0.0;
    
    // Calculate divided differences
    double dividedDiffs[n][n];
    for (int i = 0; i < n; i++) {
        dividedDiffs[i][0] = y[i];
    }
    for (int j = 1; j < n; j++) {
        for (int i = 0; i < n - j; i++) {
            dividedDiffs[i][j] = (dividedDiffs[i + 1][j - 1] - dividedDiffs[i][j - 1]) / (x[i + j] - x[i]);
        }
    }
    
    // Calculate the derivative value
    double xProduct = 1.0;
    for (int i = 0; i < n; i++) {
        result += dividedDiffs[0][i] * xProduct;
        xProduct *= (target - x[i]);
    }
    
    return result;
}

int main() {
    int n; // Number of data points
    printf("Enter the number of data points: ");
    scanf("%d", &n);
    
    double x[n], y[n]; // Arrays to store data points
    
    printf("Enter the data points (x y):\n");
    for (int i = 0; i < n; i++) {
        scanf("%lf %lf", &x[i], &y[i]);
    }
    
    double target; // The point at which derivative is to be calculated
    printf("Enter the value of x for which you want to calculate the derivative: ");
    scanf("%lf", &target);
    
    double derivative = newtonDividedDifference(x, y, n, target);
    printf("The derivative at x = %.2lf is: %.4lf\n", target, derivative);
    
    return 0;
}