Let F, G: R3 R3 and f : R3 R be differentiable. Prove the following

Question:

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) × (F + G) = ( × F) + ( × G)
b) × (fF) = f( × F) + (f × F)
c) ∙ (fF) = f ∙ F + f ∙ ( ∙ F)
d) ∙ (F + G) = ∙ F + ∙ G
e) V ∙ (F × G) = ( × F) ∙ G - ( × G) ∙ F