2. Let r > 0, let a ERn, and suppose that 9 : 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 = fog are given by oh og ox.

(a) = \1 f(g(a)) . ox. (a)

J J 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 0 g)(a)) = det(D f(g(a))) det(Dg(a)).