OK then. First we should state the MVT (mean value theorem) for integrals.

Let f be a function continous on [a,b] and differentiable on (a,b). There exists such c that satisfies,

Now we can work on the problem.

We know that . We have to find . Let

By the definition of derivative,

As ,

Oh, we can use the MVT on the expression in red =)

As h approaches x, this limit will go to .

Feel free to ask anything that wasn't clear to you.

Good luck on your second question