Depends where it broke, but if fluid is leaking it sounds like the yoke that joins the driveshaft to the transfer case. That would make it transfer case fluid. Not likely to be transmission fluid. Not a common failure, but this is why you have a warranty.

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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