Derivative of inverse

Just as in one variable we have
$(f^{-1})'(y) = [f'(x)]^{-1}$,
you get the same thing here:
the derivative of the inverse is the inverse of the derivative
(at the appropriate point):
they commute.

Again, this is deeply related to the chain rule;
the big point being that it's a -homomorphism-.
(product and inverse)
