Prove the identity, assuming that the appropriate partial derivatives exist and are continuous. If f is a scalar field and F, G are vector fields, then f F, F • G, and F x G are defined by
(f F)(x, y, z) = f (x, y, z) F(x, y, z)
(F • G)(x, y, z) = F(x, y, z) • G(x, y, z)
(F x G)(x, y, z) = F(x, y, z) x G(x, y, z)

div(∇f x ∇g) = 0