Understanding Multivariable Taylor Expansions with Vector Components

[roeb]

Homework Statement

I'm having a hard time following a taylor expansion that contains vectors...

http://img9.imageshack.us/img9/9656/blahz.png
http://g.imageshack.us/img9/blahz.png/1/

Homework Equations

The Attempt at a Solution

Here's how I would expand it:

-GMR/R^3 - GMr/R^3 + 3GMR/R^5*(R + r) + 3GMR/R^5(r + R)
So you take d/dR(R^2 + r^2 + 2r dot R)^5/2 and then take d/dr ?
I am basing my knowledge of multidimensional expansions off of what wikipedia is telling me, but I can't quite see how that r dot R term comes about

Anyone have any ideas?

 

[tiny-tim]

Hi roeb!

Hint: the denominator is R_e³(1 + 2R_e.r/R_e² + o(r²))^3/2