Let r > 0, let a Rn, and suppose that g: Br(a) Rm is differentiable at a.

Let r > 0, let a ˆˆ Rn, and suppose that g: Br(a) Rm is differentiable at a.
a) If f: Br(g(a)) †’ R is differentiable at g(a), prove that the partial derivatives of h = f o g are given by

for j = 1, 2,...,n.
b) If n = m and f: Br(g(a)) Rn is differentiable at g(a), prove that
det(D(f o g)(a)) = det(Df(g(a))) det(Dg(a)).

Transcribed Image Text:

a g rj ah (a) = Vf(g(a)) . ari 0x (a) i