Thank you haruspex for responding. The partial derivatives I said equal zero could be my mistake, but please explain how a vector with constant components in cartesian coordinates can have nonzero partial derivatives in cylindrical coordinates.
I have a larger problem involving divergences and curls, but the correct answer requires ∇°B (divergence of B) = 0. I understand the proof of this in Griffiths, but the definition of divergence in cylindrical coordinates is:
After using the product rule to split the first term, we get the...