I have a drive line issue. The differential makes noise during take off or on hills

What is your question?

I have a 05 Trailblazer with the strait 6cly.I have a issue with a noise usually from taking off at intersections. And mostly on small hills or stop and start ups. When I add power to drive line I hear almost a metal screeching to a rear differential gear grinding noise. This is only at a stand still to take off. If you add power while vehical is in motion I don't hear or feel any problems. The u joints are fine. There is no steady noise. Just like I said it's almost sounds like a metal streeching noise. I can also feel it in the rear end. Thanks

What makes this problem better or worse?

When the vehicle is warm or at normal opperation temp.

How long has your 2005 Chevrolet Trailblazer had this problem?

A few months