Which functions are in the same equivalence class as the

Question

(Requires calculus) a) Let n be a positive integer.

a) Show that the relation R on the set of all polynomials with real-valued coefficients consisting of all pairs (ƒ, g) such that ƒ (n)(x) = g(n)(x) is an equivalence relation. [Here ƒ (n)(x) is the nth derivative of f (x).]

b) Which functions are in the same equivalence class as the function ƒ (x) = x⁴, where n = 3?