For these sorts of problems, you have to kind of "reverse the order" of evaluation. Take f(x) = (x^2 - 24) / (x+2). The last arithmetic operation you would do in evaluating the function at a point would be the division. Therefore, that's the first thing you differentiate. What is the quotient rule?
For the second function, you work from outside in. You'll need the chain rule as well as the product rule. What do you get?