I wrote this worksheet for my Precalculus/IB students. It is a series of exercises for applying the product rule to find derivatives of products of two functions. While it does not go into the "why does this rule work/ where does this rule come from," it does have them justify that it works for products of polynomial functions, which they can expand and to which they can apply the power rule, to verify that the product rule does, in fact, work.
I use this activity within cooperative groups, a