MHB Application for Derivative of Inverse Functions?

[pflo]

Why are derivatives of inverse functions important?

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.

 

[chisigma]

Why are derivatives of inverse functions important?... 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?...

In my opinion the great majority of 'students' [comprising math's students...] have a 'mathematically incompatible' mind... in most cases the inverse function doesn't have an 'explicit expression' and the knowledge of its derivative is the only way to arrive to an effective computation of it...

Kind regards

$\chi$ $\sigma$