8. Let F, G : R3 --+ R3 and f : R3 --+ R be differentiable. Prove the following analogues of the Sum and Product Rules for the "derivatives" curl and divergence.

(a)

(b)

(c)

(d)

(e)

\7 x (F + G) = (\7 x F) + (\7 x G).

\7 x (f F) = f (\7 x F) + (\7 f x F).

\7 . (f F) = \7 f . F + f . (\7 . F).

\7. (F + G) = \7. F + \7. G.

\7 . (F x G) = (\7 x F) . G - (\7 x G) . F.