1990 Other BMW Models differential?

I recently had some work done on a 90 735il. This included aotomatic steering box, transmission rebuild, drive shaft bearings, motor mounts, spark plug and spark plug wire replacement. The noise I will describe may have been present in some form prior to the work but I'm not sure. At approximately 30 mph there is a distinct whirring sound especially when descellarating, with or without braking, and also when accellerating. It sounds like an electric motor running at a very high speed. The car runs fine at higher speeds and the repair shop rechecked the tranny and claims it is ok. He suspects rear end or tire problems. In surfing the internet the diagnosis by various entities seems to point to differential gear problems.

1. Can the problem be more accurately diagnosed?

2. What is involved (costs to replace the differential?

Thank you.