1. The problem statement, all variables and given/known data The curl satisfies (A) curl(f+g) = curl(f) + curl(g) (B) if h is real values, then curl(hf) = hcurl(f) + h'·f (C) if f is C2, then curl(gradf) = 0 Show that (B) holds. 2. The attempt at a solution I'm not quite sure how to interpret the "h is real valued" part. Does it mean that, as is, h is a scalar quantity and its derivative is a vector? Any help is appreciated. - - - - So far I've been reviewing the definition of curl. I let f = f(x, y, z) = (f1(x, y, z), f2(x, y, z), f3(x, y, z)) hf = (hf1(x, y, z), hf2(x, y, z), hf3(x, y, z)) curl(hf) = (D2(hf3) - D3(hf2), D3(hf1) - D1(hf3), D1(hf2) - D2(hf1)), but I don't see where this route is taking me.