Differentiating modulus in electrostatic potential

[kryky]

Hi,

I am trying to do the multipole expansion of a point charge away from the origin, I can't understand Legendre polynomials so want to do it in Cartesian but when I try to Taylor expand
the $$\left|\frac{1}{\vec{r}-\vec{r'}}\right|$$ I am not sure how to handle the modulus.

Any help appreciated.

 

[ApexOfDE]

Griffith's Classical electrodynamics p.147 has a detailed explanation for multipole expansion. You may take a look on the that book.