Secret Message to the Publishers of Calculus Books

When introducing the rules of differentiation, please, please, please do not make the product rule the second rule taught. (Obviously the first rule is going to be the "famous one" that even my mother remembers.) When you do it this way, none of the problems actually need the product rule.

Here's my suggestion: Teach the power rule first (obviously). Then teach the "generalized power rule" (special case of the chain rule). After that teach the product and quotient rules. Sure, there's the downside that students won't learn the quotient rule because after learning the product rule they can write everything as uv^-1, but we can't have everything.