Royal Purple has a new and unique diff fluid that is 75-140w so it can be used in a wider temperature range than any other fluid I have seen. Most all synthetics do NOT require you to use the LSD additive although I have heard from those using Mobil 1 that have had to add it to stop the chatter (and excessive wear on the clutches).
Be sure to use teflon thread sealer at least on the front bolt you remove to drain or it will wick down the threads and drip. I use it on all plugs I remove that hold in fluid.