Teaching Derivatives of Inverse Functions - The Easy Way!

I told someone last week that I'd send them a summary of how I teach derivatives of inverse functions, so I figured I would post it here too in case it could also help others.  My first year teaching AB this felt like a small formula that kids would need to have memorized for the potential of 1(or maybe 2) questions on the AP exam- ugh. I had multiple teachers my first year tell me just to skip it....it could be left out and no one would be the wiser. I really struggled with that idea, so I stumbled my way through it.

I was lucky enough to have another teacher share their strategy for teaching derivatives of inverses with me and I've never looked back. My kids rock at it now and it makes sense to them- not another formula to memorize. We are building on the idea of inverses from previous courses....that if (a,b) is a point on f we know (b, a) must be a point on the inverse of f.

I've also linked to a discovery activity where students see that derivatives of inverses are reciprocals by looking at linear functions. It's simple, but lets them do a bit more of the heavy lifting.

Derivatives of Inverses Discovery Activity & Directions with Table

Happy deriving!