sometimes when I drive my 2007 mustang around I like to give it a moderate amount of throttle because it sounds good, but when I lift off the throttle it makes a loud thump coming from the rear of the car. I have an automatic if that makes a difference, about 3000 miles, and it seems to happen more at speeds below 15 mph. If I change the gear fluid to like Royal Purple would that fix it?

 

I drive an an auto and have never heard a thump, are you sure its differential related and maybe not suspension or just something that has come loose? I'd take it to the dealer show him the problem and have them find and fix it.

 

Me and my dad were thinking maybe because I give it a lot of gas then let off before it switches to second gear and maybe that messes up the system. Anyway its pretty loud and doesn't always happen.

 

Try letting off after the shift and see if it happens consistently. If so, take it back to the dealer.

 

Give it gas, then let off several times in a row. If it klunks at each event it is driveline slack...probably our great 2-piece driveshaft. Mine does it a lot.