I think one of the hard things for students is to pick apart a complicated function while doing a derivative when you need a combination of derivative rules. Do we use product rule first here or chain rule? Even more crippling is when they don't realize that you need a rule in the first place! We did an exercise today for about 15 minutes where I put up a function on the board and they had to write down the order of the derivative rules they would need to use, but just in a string of letters (see above for example… P is product, Q is quotient, T is trig, C is chain and E is power – E for exponent since P was taken). I wrote up all their answers and then revealed the correct one and we talked a bit about each one. We never actually took the derivative of them, just thought about what rules we would need. Overall, it was positive because it was a total change of pace, but who knows if this actually helped!
One thing I did in the past was give them a bunch of slips with functions on them and they sorted them on whiteboards into categories based on the rules they would need. I enjoyed this because they all did it in different ways (bales, categories, Venn diagrams!). Anyone have anything else for getting kids to recognize when to use derivative rules, besides just taking tons and tons of derivatives?