Last year I created a calculus worksheet (here) where kids had to differentiate various functions made up of other functions that were not necessarily explicitly defined. Like, find y’ if y=cos(f(x)), where f is a differentiable, real-valued function of x. What about y=f(cos(x))? Things like this. I couldn’t find anything like this in their textbooks but I did see questions like this pop up a lot on AP Exams.
So, I gave my kids this same worksheet today, and they did absolutely beautifully on what I think are not extremely straight-forward problems.
One kid said he was having a hard time with the chain rule until today. “And now I totally get it!”
Yayyyy!! I get very excited when I can create practice for kids that really helps shed light on a particular topic.
Also, this text I got from my baby sister (who’s in precalc at a neighboring school):