Taylor Expansion (multivar)

1. The problem statement, all variables and given/known data
I'm having a hard time following a taylor expansion that contains vectors...

http://img9.imageshack.us/img9/9656/blahz.png [Broken]
http://g.imageshack.us/img9/blahz.png/1/ [Broken]
2. Relevant equations



3. 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?