Chapter 4 - Vector Spaces - 4.3 Subspaces of Vector Spaces - 4.3 Exercises - Page 167: 6

$W$ is a vector subspace of $V$.

Since the sum of differentiable functions is differentiable and the multiplication of a differentiable function by a scalar is differentiable, then $W$ the set of all functions that are differentiable on $[-1,1]$ is a vector subspace of the set of all functions that are continuous on $[-1,1]$.