Question: Assuming sufficient differentiability, show that (a) curl (u + v) = curl u + curl v (b) div (curl v) = 0 (c) curl (fv)

Assuming sufficient differentiability, show that

(a) curl (u + v) = curl u + curl v

(b) div (curl v) = 0

(c) curl (fv) = (grad f) × v + f curl v

(d) curl (grad f) = 0

(e) div (u × v) = v • curl u - u • curl v

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