Manchester City delivered a ruthless attacking display to rout
Sergio Aguero volleyed home an acrobatic goal in the 16th minute, Yaya Toure doubled the lead in the 45th minute and Aguero scored his second goal in the 47th. Samir Nasri's 50th-minute goal completed the burst at the start of the second half.
Wayne Rooney scored United's goal on a curling free kick in the 87th
"It's horrible to lose the derby - it's always horrible. It's worse when you lose in this way," United captain Nemanja Vidic said.
While City gained a big win under new manager Manuel Pellegrini, who replaced Roberto Mancini after last season, United has struggled since Ferguson left after nearly 27 years. United (2-2-1) is eighth with seven points under new manager David Moyes, its poorest Premier League start since 2004-05 season.
"I've made them aware of what I think," said Moyes, whose team earned just one point from matches against Liverpool, Chelsea and City.
Arsenal leads on goal difference over Tottenham (both 4-1), with City (3-1-1) two points back, ahead of Chelsea and Liverpool on goal difference.
Mesut Ozil, the playmaker acquired from Real Madrid for 50 million euros ($66 million), assisted on all of Arsenal's goals in a 3-1 win over Stoke. Aaron Ramsey, Per Mertesacker and Bacary Sagna scored for for the Gunners.
Paulinho scored in the third minute of second-half stoppage time to give Spurs a 1-0 win at Cardiff.
Di Canio became the first Premier League manager to lose his job this season when he was fired by last-place Sunderland (0-4-1).
BARCELONA, Spain (AP) -
Angel Lafita but the visitors ahead in the fifth minute, but Pepe scored from a rebound in the 19th, Ronaldo converted a penalty kick in the 33rd, set up Francisco "Isco" Alarcon in the 59th and added a goal in stoppage time.
Real Madrid (4-0-1) is third with 13 points, two behind Barcelona and Atletico Madrid (both 5-0).
BERLIN (AP) - Stuttgart striker Vedad Ibisevic missed a penalty kick with the last shot of the game as the home team tied
Marco Russ stabbed the ball to the roof of the net from a corner kick to put Frankfurt ahead in the 14th minute, but Timo Werner scored for Stuttgart level a minute later.
ROME (AP) - New Jersey-born forward Giuseppe Rossi scored his fifth goal in six matches this season, helping Fiorentina to a 2-0 win at Atalanta in the Serie A.
Matias Fernandez scored in the 41st minute, and Rossi added his fourth league goal in the 69th.
Roma (4-0) beat Lazio 2-0 in the Derby della Capitale on Federico Balzaretti's 63rd-minute goal and Adem Ljajic's penalty kick in the fourth minute of stoppage time.
Napoli (4-0) won 2-1 at AC Milan (1-2-1) on goals by Miguel Britos and Gonzalo Higuain. Mario Balotelli scored in second-half stoppage time for Milan after his 61st-minute penalty kick was blocked by goalkeeper Pepe Reina. Balotelli, who had been perfect in 21 previous career spot kicks, got his second yellow card after the final whistle in a penalty for protesting. He is suspended for Milan's next league match.
Inter Milan (3-0-1) routed Sassuolo 7-0,
Boyd has five goals in six league matches this season.
PARIS (AP) - Paris Saint-Germain tied 1-1 at home against Monaco in a matchup of France's big spenders.