Manchester United registered its win against Sunderland. It defeated Sunderland by 1-0, this margin which I think for a champion who is on its way to defend a title is not enough. If they really want to win the title they have to play well and score more goals.
On the other hand Liverpool defeated Derby by 6-0, the higher ever goal difference by Liverpool in this league. With this sort of play they are showing their potential to win the league title.
Whereas Chelsea faced a first defeat in this league. Aston Villa defeated Chelsea by 2-0 showing that in this league the team on the bottom of the league are also growing stronger to be a strong competitor in winning the title.