18/08/15 13:32:46.08 SQV3T5wE.net
Theorem 7.4.
Let A be open in R^n; let f : A -> R^n; let f(a) = b.
Suppose that g maps a neighborhood of b into R^n, that g(b) = a, and
g(f(x)) = x
for all x in a neighborhood of a. If f is differentiable at a and if g is differentiable at b, then
Dg(b) = [Df(a)]^(-1).