Question: I came across a question in our book that states: Let Q(x) = N(x) / D(x) Then re-write Q(x) in a form that can utilize the Power and Product Rules. Use this rearranged form to derive the Quotient Rule.

The Quotient Rule can be derived from the Power Rule and the Product Rule.

One must also use the chain rule too, right?

I would agree that you also need the chain rule, however I seem to recall a text that proved the chain rule before the power rule and then stated the power rule as

In any case I think that the author is looking for the argument