Derailer - Rear - Shimano XT 10-speed
Shadow is Shimano-talk for a rear derailer whose body doesn't stick out as far, and is therefore theoretically less likely to run into a rock. It was probably an overreaction to an incident like that, and in a rare circumstance it has to work, but for it to "work" you'd have to pass the rock with your body and legs, and then turn a corner just the wrong way and hit a rock.
The "shadow" rear derailers don't have barrel adjusters. That's a bigger deficit than the "shadow" part is a benefit, but as long as you have a RapidFire shifter with a barrel adjuster, that's not big deal.
On the other hand, if your shifters don't have a barrel adjuster, you shouldn't get this derailer. And...it's a 10sp model, and if you have a 8sp chain, the chain will rub on the cages. It'll shift, but it'll also drive you nuts with noise. It'll work great with 9 speed chains.
Both shifts to 36t in back and work up to 10 speed index Shimano road STI systems.
RD 772 GS or SGS shadow. GS means medium cage length in Shimanoese and SGS means long cage. Get the SGS long if you have a triple crank; get the GS medium if you're doing a double or single ring crank.