Thread: Subspaces

Hi Everyone! I hope someone can help me because I REALLY need it!! Thanks!
Two Questions:
(1) Is the set of all differentiable real-valued functions defined on R a subspace of C(R)? Justify your answer

(2) Prove that if W is a subspace of a vector space V and w1,w2,...,wn are in W, then a1w1+a2w2+...+anwn in W for any scalars a1,a2,...an

For #1, what does it mean to be a subspace?