Actually, it's a special property of the quotient rule:
I only used the quotient rule.
Well, I'll throw my hat in the ring and agree with Colby. In my opinion, the use of the chain rule as explained by Colby does not constitute a special case of the quotient rule. It's a legitimate third method - and, arguably, gets to a simple answer faster and with less chance of error.
By the by, I'd be disinclined to present first principles for getting the derivative for this sort of question. But it is always nice to see it.