First of all I would make sure it is the diff leaking. I would clean off all of the engine and then idle the engine for a few minutes and if no leaks appear, drive it around the block and then check again. There are many little leaks that can happen and can be mistaken for something else. Some of the more common leaks that will do what you are talking about is the power steering. Both the O-ring under the tank, or a pressure or return line. They can be very small leaks and drip down and look like something else leaking. Try cleaning the engine and see where the leak is and then we can go from there. Good luck.
