Product Rule via Geometry

I was researching some justification for the product rule, and I am amazed that I never knew this before. It's so obvious (and much easier) if you approach it from a geometric perspective, thinking about how the length, width, and area of the rectangle change. Here are my visuals in thinking through this process, and also how I am planning to scaffold it for my kids. I named the product formula A = ... because I think that is most intuitive to think of that product as the Area that changes as a result of each length or width function changing.

Do you introduce product rule this way? Do you have recommendations for me?