ive been trying to understand a few of the identities my professor gave me and i can get a few of them down such as(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\nabla(\vec{A}\vec{B})=\vec{B}\nabla\vec{A} - \vec{A}\nabla\vec{B}[/itex]

and i can break it down through cartesian and product rules but when i try to do

[itex]\nabla X (\vec{A}ψ) = \nablaψ X\vec{A} + ψ\nabla X \vec{A}[/itex]

where ψ is a scalar

i get lost.

i broke down the LHS into a matrix, and did product rule.

but then looking at the RHS, it doesnt seem like it would come together, not unless there may be a step or a rule im overlooking. any insight?

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# Understanding vector calculus proofs

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