Strange squeak when driving

RTAB's. Just changed mine today in my 2001 300ci and what a difference in ride. Could be the torque tweaking the bushing back and forth.
Your due anyway if you've never changed these bushing's and not much else can squeak but a worn bushing and these are most common culprit.

I replaced using Lemfoerder brand, 2001 M3 part number is now recommended for our 330's. Car tracks and handles much better now. Check out Pelican parts and real.oem for the part number of these heavy duty rubber RTAB's, some use poly but I did not want to worry about the squeeks they are prone to.

or search for RTAB and you'll find a lot more info.

it loads up and tweaks in first gear, then relaxes when you stop. It is the back and forth motion. doesn't get a chance to relax between gears only when you stop or take the load off of the differential.

take a look at this link: http://www.realoem.com/bmw/partgrp.do?model=BN53&mospid=47713&hg=33&fg=30

The rear differential applies torque to several bushing's on both the carrier and rear axle support. It is one of those Bushing's. I am just guessing RTAB ( #4 on axlw support) since it is the one most complained about making noise and wearing out. It could be #9 Bushing on the carrier too. I believe it takes the side load from the diff..that would also explain first gear squeek only.

Get under it and inspect / see the logic of what Bushing takes the torque when you engage first gear...to see if you see anything obvious wear and tear wise. If you had access to a lift it would be good to have someone go from stop to 1st, reverse to first while you were under it listening for the culprit and also witnessing the torque on the bushing's. If you are brave you can do it on 4 jackstands with two floor jacks under there for back - up, just be safe. It can be done but not recommended by safety experts....