Let V be the vector space of real-valued continuous functions with ordered basis S = {sint, cost}

Question:

Let V be the vector space of real-valued continuous functions with ordered basis S = {sint, cost} and consider T = {sint - cost, sint + cost}, another ordered basis for V. Find the representation of the linear operator L: V → V defined by L(f) = f' with respect to
(a) S;
(b) T;
(c) S and T;
(d) T and S.