When Scott told Stiles Derek had died the world did not suddenly stop turning. There was no 'oh my God, what are we going to do' type moment. There wasn't even a 'you're lying, he's not dead' argument either. He just didn't allow himself to care. If he did, if he took a moment to pile on Derek's death to the already shit storm his life had become, he would completely lose it.
Heather was dead, a fricking Darach thing was running around killing people, the FBI seemed to be breathing down his father's neck because of the apparent 'serial killer', and, oh yeah, to top it off a freaking pack of Alphas decided to enter town. It was one bad thing on top of another, too much for Stiles to ignore. To put icing on the cake, it seemed Scott had a giant freaking hole in his side because of the things that killed Derek.
To cope, he was going to focus on the things he could handle. Scott's side for one, perhaps being a major catalyst in finding the Darach for another; those were the things he could fix, the things he could do something about. He couldn't change the fact that Derek was dead; he couldn't bring the guy back no matter how much he wanted to at least try.
It pained him to do it, but he had to ignore Derek's death, push it to the very back of his head, just until he had a moment to breathe. A moment when he wasn't completely terrified of losing someone else he cared for, someone else the pack might need, his own life. That was all he needed; just a moment.
It seemed to bother a lot of fans that Stiles didn't seem to care about Derek's apparent death, so I decided to write an explanation. Just something to keep my sanity (or what's left of it) in tact.
Thanks for reading, leave me a comment if you want, and I don't own Stiles.
See ya!