Derek didn't have time to think. He took off after the unsub, knowing this was their only chance at bringing him in. He ran as hard and fast as he could.
This guy was a cop, but what he didn't know was that Derek had been one, too. He had that advantage. He knew that the uniform made people listen. Made them believe this guy when he fed them lies.
He was still in pursuit twenty minutes after everyone else had stopped searching. This guy had terrorized people for long enough. It was dark, but Derek's adrenaline was flowing.
He moved carefully and efficiently, and when he finally located the unsub, bleeding from a gunshot on top of a roof, Derek considered it a victory.