Show that derivation is linear?

I'm completely stuck on this one:

"Derivation $\displaystyle Dp = p'$ defines a transformation $\displaystyle D : P_2 \rightarrow P_2$. Use the definition of linear maps and the properties of derivation to show that D is linear. Describe the codomain and the range of D. What is the kernel of D? What are the dimension of range(D) and kernel(D)? Is the map onto? Is it one-to-one? Is it an isomorphism?"

Where should I start? What should I read in order to understand this? Is this a problem that is understood simply through general experience with calculus and linear algebra?