Let f: X be differentiable at x and g: Y be differentiable at

Let f: X → ℜ be differentiable at x and g: Y → ℜ be differentiable at y. Then their product f g: X × Y → R is differentiable at (x, y) with derivative
Dfg[x, y] = f(x)Dg[y] + g(y) Df[x]