function dy_dx = forward_diff(x, y)
   
    N = length(x);                      
    h = x(2) - x(1);                     
    dy_dx = zeros(N, 1);                 
    
    for i = 1:N-1                        
        dy_dx(i) = (y(i+1) - y(i)) / h;  
    end
    
    dy_dx(N) = dy_dx(N-1);             
end