Prove (a) - (d) vector differential identities

Vector differential identities. Let f and g be scalar valued functions from R' to R and F and G be vector fields from R' to RS. Assuming that all required first, second, and sometimes third, partial derivatives exist and are continuous, we have lots of identities. We ask you in Problems 3.56-3.59 to verify the following identities. In (e) and (f) we define F . VG = fiGx + f2Gy + f3Gz = (DG)F. (a) V(fg) = fVg+8Vf (b) div (fF) = fdivF + F . Vf (c) div (F X G) = (curlF) . G-F . curl G (d) curl (fF) = fcurlF + (Vf) XF