I run synthetics in the engine (5W30), transfer case (ATF+4), and differentials (75W90). Any major brand. If differential oil says it has the added ingredients for limited slip you can still use it without any problems.

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2018 BMW X5 Xdrive 50i (M Package)
2002 BMW X5 4.4i /w Sports Package (Sold)
2001 Dodge Ram 1500 Laramie 4x4
2003 Jeep Liberty Limited 2x4