I wasn't suggesting that you were invalidating an otherwise correct answer so if I gave off that misconception then I apologize. The reason I thought most would prefer the product rule is because it doesn't directly incorporate a denominator term which tends to make a rational expression more complicated "looking". Don't get me wrong, the quotient rule should be mastered by any student taking a Calculus course but for post-course practices when both techniques have been mastered I personally prefer to interpret the quotient as a product so as apply the product rule rather than the quotient rule. Obviously, this little "trick" can not be done in every case but in situations where situable and time savings are available then I would take it.