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, and I circulate to make sure they are getting the purpose of the questions.
The file includes spiral review problems.
For this worksheet, I expect students to show their work on a separate sheet of paper.
Please download the pdf preview file first, so you can see exactly what's included; the product file is a word document, which you may personalize for your students.