def partial_difference_quotient(f, points, v, i, h):
    """compute the ith partial difference quotient of function f w.r.t to ith position of v"""
    
    #add h to just the ith element of v
    w = [v_j + (h if j == i else 0) for j, v_j in enumerate(v)] 
           
    return (f(points, w[0], w[1]) - f(points, v[0], v[1])) / h