Suppose f (x) is a function such that for some positive integer n, f has n linearly dependent derivatives. In other words, if f(x), f'(x), ..., f(n-1)(x), f(n)(x) are all linearly dependent functions, then f(x) is expressible in terms of a, xk, eax, sin(ax), cos (ax), and any combination of such functions, where a is a constant and k is a positive integer. Prove this statement.