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My students are giving me questions like:

When would using the theorem be useful? Can't you just find the inverse function and take its derivative?

I'm sure many of you know the type of question: "Who cares?"

My answers are that the theorem is useful in proofs (e.g. derivative of the natrual log) and that sometimes you can't just find the inverse and take its derivative. But the examples I give are less than convincing - they end up being examples where you could just differentiate the inverse.