Simple calculation about Magnetic induction

[BREAD]

Homework Statement

Homework Equations

The Attempt at a Solution

Why does the second term become zero??

 

[kuruman]

Why does the second term become zero??

Because it does not exist. If, in the previous equation, you substitute the gradient with some vector $\vec{V} = \vec{\nabla} \left ( \frac{1}{|\vec{x}-\vec{x}'|} \right )$, you will see why. There is no vector identity in the front of the book to be used.

 

[vela]

Why does the second term become zero?

The derivative $\nabla$ is with respect to $\vec{x}$, not $\vec{x}'$.