# Understanding vector calculus proofs

1. Oct 1, 2011

### filipin0yboi

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

$\nabla(\vec{A}\vec{B})=\vec{B}\nabla\vec{A} - \vec{A}\nabla\vec{B}$

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

$\nabla X (\vec{A}ψ) = \nablaψ X\vec{A} + ψ\nabla X \vec{A}$
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?