Whine versus a wheel bearing
Read the two symptom lists side by side. The differential page says whine from the rear, plus the scheduled fluid service. The front wheel bearing page says a humming or growling that rises with speed. The rear bearing page adds play when you rock the wheel, and a noise that changes when you turn. If the noise changes in a turn, start with Front Wheel Bearing / Hub or Rear Wheel Bearing, and with the BMW Whining, Humming and Growling Noises: Causes and Costs. If it is a steady whine from the back, start with Rear Differential Fluid Change.
The fluid service
Owners describe a rear drain and fill as roughly a 20 to 30 minute job on a lift. Ask whether the quote is the rear only or a bundle with the front differential and the transfer case. Confirm the fluid by VIN on M cars and limited-slip differentials. The 60,000 mile context is in the BMW 60,000 and 100,000 Mile Service Costs.
Low fluid from axle seals
On the G01 X3, leaking rear differential axle seals show as oil residue around the axle shafts, often a seep a tech notes during a tire or brake visit, and a whirring from the rear at speed if the fluid gets low. That is G01 X3 Rear Differential Axle Seals, and our US prices there are dealer prices. The front differential can make noise from the front axle area (Front Differential Fluid (xDrive)).
Shudder is not whine
Binding or shudder on a tight turn is the transfer case fluid or the actuator, covered in the BMW xDrive Transfer Case Shudder. A clunk, rather than a whine, is more often the guibo (BMW Guibo and Flex Disc Replacement).