Jack your car up in the air, look under it, you will see the differential in the center. Now look under the diff, you will see a hex-head plug. This is the differential drain plug. In order to drain the old oil, we will need to remove this plug. Slide a drain tray under this plug. Now, look at the back of the diff. You will see a similar plug on the rear face of the differential.. This plug is the fill port for the new differential oil.
Now, remove the fill plug first. Use a 14mm Allen key or socket to remove the two plugs. This will help relieve any vacuum built up inside the diff and make it easier to drain the old fluid out. Next, remove the drain plug from the bottom.
Immediately, the differential oil will pour out. It should take a few minutes for all the fluid to drain out.
Once all the old fluid is out, re-install the drain plug and tighten. Next you will want to measure out the correct amount of fluid for the differential. You will want to measure out 1.8 quarts of oil. BMW recommends you use BMW SAF-XO Synthetic Oil for differentials without limited slip, or use BMW SAF-XLS Synthetic Oil for differentials with limited slip. Royal Purple Synchromax is a good alternative.
Now, use a siphon or pump to get the new fluid into the fill port on the rear of the differential. When the fluid starts to pour out of the top of the fill port, the differential is full. Remove the pump/siphon, and re-install the fill port plug and tighten using a 14mm Allen key.