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