its a little tricky. but if you can get the center stud mount off it will come right out
1st get your truck on jack stands. Make sure it is sturdy because you may be under it for awhile.
2nd drain oil and remove cv's. You dont have to take them out of the knuckle, But you will need to undo the Lower ball joint bolts
3rd make sure everything is disconnected. There should be breather, couple electronic plugs and maybe a vacuum line or two. Your 01 may be all electronic
4th get a floor jack under the diff. remove the 12mm allen on the bottom rear. then remove the two front bolts.
5th let that jack down an inch or so. Try and get the two bolts off that hold the rear stud/mount to the diff. They are 17mm and hard to get to.
6th take it out.
Once you have it out you will need to slip the case. To do so you should remove the entire add tube to expose the stub shaft. You will an an E-torx. i forgot the size. After removal of that you will see the add stub shaft on the passenger side of the clam shell. This is held in just like the cv joints (it has a clip) So get a pair of crowbars and pop it out of the carrier (it clips into the carrier in the diff)
Once you have that all removed you can slip the case. If you do not take the add tube off and split the case the carrier will stick to the Passanger/add side of the diff. This may be fine for you if you only want to inspect the case/ring&pinion.
If you end up wanting to remove the carrier and try to pop it off the stub shaft from the inside you will likely pull the carrier bearing race out of the diff (this happened to me when i tired to shortcut disassembly when i put my front locker in) Then i still had to get the stub shaft off the carrier. then had to be extra careful to put the stub shaft back in the add tube followed by the shims and then re-press the carrier bearing race into the clamshell side.
Good luck when you get into it most of this should make some more sense
