Suppose that V is open in Rn, that f, g: V → R3, and that a ∈ V. If f and g are differentiable at a, prove that f × g is differentiable at a and
D(f × g)(a)(y) = f(a) × (Dg(a)(y)) - g(a) × (Df(a)(y))
for ally ∈ Rn.