2. Let V be open in Rn, let a E V, let f,g: V ---+ R3, and suppose that f and 9 are differentiable at a.

(a) [CROSS-PRODUCT RULE] For the case n = 1, prove that fxg is differentiable at a and

(f x g)'

(a) = f

(a) x g'

(a) + f'

(a) x g(a).

(b) What happens to part

(a) when n > I?

(c) Suppose that f

(a) = (2,1,2), g

(a) = (1,2,1), Df

(a) = [~ ~ ~], and Dg

(a) = [-~ _°1 ~].

1 1 1 1 ° -1 Find D(f· g)(a)(I, 1, 1) and D(f x g)(a)(l, 1, 1).