Today I talked a little bit about implicit differentiation with my son. We are following the progression in an old copy of Stewart’s Calculus book that I have (the 3rd edition) and section 2.6 discusses implicit differentiation.

After we had an introductory discussion this morning, Patrick Honner sent me this message:

Throw x^2 – 2xy + y^2 = 0 at some point. Always a puzzler!

Since my son had a half day of school today and I’m going to be working late tonight, I talked through the problem with him when he got home from school.

As I mention in this video introducing the problem, he’s not done any implicit differentiation problems on his own, yet, but you have to start somewhere!

By the end of the first video he’d found a value for the derivative, but now we had to interpret what he found – wow is it interesting listening to a kid trying to wrestle with calculus ideas for the first time!

To wrap up, I showed him some potential puzzles that are hiding behind the scenes in calculation – though I didn’t resolve these puzzles for him.

You can’t divide but you can subtract and factor i.e.

(y’ – 1)(2y-2x) = 0

Yes – that’s what I was hoping to get to in the 3rd video,!but we didn’t quite get there.