IIRC, the proceeder for both is in the Haynes manual. But don't have one
to hand to check.

I would suggest that you not start tearing things apart until you are sure
where the problem lies.  Differentials can become very noisy without
suffering catastrophic failure so you still have plenty of time to come up
with the correct diagnosis.  I drove my noisy '84 318i over 10,000 miles
before I replaced the failing differential at 300,000 miles.  If it is the
differential you should be able to change the noise with the gas pedal.
High throttle settings should produce more noise which I think you have
already stated.  It should also make a very different noise under engine
braking than it does under accelleration.  The noises should be most
noticeable as you start off from a dead stop and be kind of a waa waa waa at
very low speeds.  Differential noises also tend to disappear into the
background noise at higher speeds while wheel bearing noises tend to
resonate the springs and become a 'low tone' at higher speeds.  After you
have the car jacked up and the drive shaft and axles disconnected, it will
be very easy to turn the differential shafts by hand to see how rough it
feels/sounds.
I replaced mine with a $150 unit from a wrecking yard.  At the time a
rebuilt unit cost $1700 and a new one from BMW $3200.  It was still
performing perfectly 40,000 miles later when I hit some black ice on a
freeway overpass in Montana and totalled the car.  Rebuilding differentials
requires special tools and skills and is not covered in any of the popular
maintainance books so I wouldn't suggest that you attempt to do it yourself.
If you decide to get one at a wrecking yard be sure to replace the seals
before you install it.  That will take a couple of hours and cost you $40.
Be sure to measure how deep the axle seals are pressed into the housing
before removing them because there is no shoulder to control their depth and
it doesn't warn you about this in Bentley.

Good Luck
Jack