I wasn't using the EXACT problem... That's just weird... I was showing the positive version of the rule... I wasn't quoting the problem at all.

I never once said that division and multiplication are different, but going from

to

requires a step that is not always intuitive. The problem sounds like he's in Calc. I. And adding a rule intuitively is not always the best way for someone to solve a problem.

The Reciprocal rule was used, and it is a version of the Quotient Rule, and that Rule was embedded in your solution through the Product Rule.