Solving a Difficult Calculus Problem: Applying the Product Rule

[exmachina]

Homework Statement

http://i.imgur.com/TSLwA.png

Homework Equations

The Attempt at a Solution

Sorry I figured it out, it was the product rule.

 

[Päällikkö]

It's not zero. That part is an identity from vector calculus, namely:
$$\nabla \cdot (\psi\mathbf{A}) = \mathbf{A} \cdot\nabla\psi + \psi\nabla \cdot \mathbf{A}$$
as in http://en.wikipedia.org/wiki/Vector_calculus_identities