Thread: boundedness and linear operators question

Hi i'm having trouble with this:

Consider a linear operator from a Banach space X to X. Let X=L2(0,1) (lebesgue space with p=2). Give an example of a (densely defined) linear operator A which is unbounded from X to X?

You could take the operator to be the operation of differentiation. Of course, you'll have to explain why it is (a) densely defined and (b) unbounded.