If it is 75w90 it would probably be fine. You could always get the appropriate oil at the dealer.

And your differentials are not limited slip, so if that oil is designed for limited slip clutch packs you don't need it.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue