77. Proof In parts (a), (b), (c), (d), (e), (f), (9), and (h), prove the property for vector fields F and G and scalar function f. (Assume that the required partial derivatives are continuous.) a. curl (F + G) = curl F + curl G b. curl (Vf) = Vx (Vf) = 0 c. div (F + G) = div F + div G d. div (F x G) = (curl F) . G - F . (curl G) (IXA)XA = [(AXA) +fAXA a f. V x ( f F ) = f ( V x F ) + ( Vf) x F g. div (fF) = f div F + Vf . F h. div (curl F) = 0 (Theorem 15.3)