Hi,

I have two energy potentials:

where is a constant vector.

Apparently the following is true:

I did this a few years back and since then my math has become rather rusty but if anyone could explain how I got the first equality I could work on the next one.

This is my working without including the constant vector:

Attempt 1:

where (,x) refers to the partial derivative with respect to x.

But then this doesn't give the desired result when applying it for all three directions.

Attempt 2 (Just blindly differentiate with respect to the magnitude r):

differentiating again with respect to r:

I've also tried the vector laplacian but it still didn't work.

Thanks for any help.

K

EDIT: I don't know why I did attempt 2 that is just 1 right off the bat.