Rear diff oil change interval in EU cars is 60 th km (37 th miles). I personally change the oil every 10-12th mile. You need 1 l of BMW diff oil (part no: 83 22 2 365 988) and 2 x Screw plug with O-ring (part no: 33 11 7 525 064).
After 35 th miles diff oil looks like this:
Oil was dark but there was not any particles or sediment.