(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The curl satisfies

(A) curl(f+g) = curl(f) + curl(g)

(B) ifhis real values, then curl(hf) =hcurl(f) +h'·f

(C) iffisC^{2}, then curl(gradf) = 0

Show that (B) holds.

2. The attempt at a solution

I'm not quite sure how to interpret the "his 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) = (f_{1}(x, y, z), f_{2}(x, y, z), f_{3}(x, y, z))

hf = (hf_{1}(x, y, z), hf_{2}(x, y, z), hf_{3}(x, y, z))

curl(hf) = (D_{2}(hf_{3}) - D_{3}(hf_{2}), D_{3}(hf_{1}) - D_{1}(hf_{3}), D_{1}(hf_{2}) - D_{2}(hf_{1})),

but I don't see where this route is taking me.

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# Proving properties of curl

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