Five things we learnt in the Premier League

The Premier League's established powers continued to flex their muscles as Manchester City, Chelsea and Manchester United all maintained their perfect start to the season with a third straight win each, while champions Leicester City and Arsenal recorded their first league wins of the season. Here are five things we learnt: City still have cross to bear Pep Guardiola's men were frequently sublime going forward in a 3-1 win at home to West Ham on Sunday, with Raheem Sterling scoring twice. But what looked like being a comfortable win became decidedly nervy for City when West Ham's Michail Antonio, against a defence still missing the re-assuring presence of the injured Vincent Kompany, headed home to make it 2-1 in the 57th minute. Other teams will have noticed how Antonio easily outjumped both Nicolas Otamendi and Gael Clichy. Liverpool need more bite up front Liverpool were the superior team in their game at Tottenham Hotspur, but had to settle for a point in a 1-1 draw due to their inability to take their chances. Despite bossing the first half, it took a 43rd-minute penalty from James Milner to put Liverpool ahead and after Sadio Mane had seen a goal ruled out for a marginal offside, Danny Rose equalised for Spurs. Having seen his team beaten 2-0 by Burnley the previous weekend despite gaining over 80 percent of possession, it was the second time in a week that manager Jurgen Klopp returned to the changing room shaking his head. Klopp has both Divock Origi and Daniel Sturridge at his disposal, but chose to align Roberto Firmino as a 'false nine' at White Hart Lane. The Brazilian won the penalty, but did not come close to scoring. Klopp has plenty of attacking options at his disposal, but he is still searching for the right combination. Rashford has the right attitude Jose Mourinho had talked at length about Marcus Rashford on Friday and denied he was ignoring him in favour of the veteran Zlatan Ibrahimovic. Even if the Portuguese was being disingenuous about the teenager, the youngster showed his confidence hadn't been blunted coming off the bench to score the only goal of a 1-0 win in time added on against an obdurate if unadventurous Hull outfit. This was an encouraging result for Mourinho, the self-styled 'Special One', and a sign that United are set to be serious title contenders for the first time since managerial great Alex Ferguson retired. Conte earns his break As Antonio Conte relaxes on the beach back home in Italy next week, the Chelsea manager will be able to reflect on a perfect start to life in the Premier League. Chelsea's 3-0 win over Burnley on Saturday maintained Conte's 100 percent record in his four matches in all competitions since arriving at Stamford Bridge in July. Conte's hectic schedule, leading Italy to the Euro 2016 quarter-finals and then immediately taking charge of Chelsea, has left the former Juventus boss admitting he needs a rest to recharge his batteries. So he will fly home to see his wife and daughter in good spirits after goals from Eden Hazard, Willian and Victor Moses put the Clarets to the sword. Wenger rides out another storm Assailed by the taunts of a growing army of doubters, Arsene Wenger enhanced his reputation for sheer resilience by leaving Vicarage Road on Saturday with with 3-1 win against Watford that, temporarily at least, silenced his critics. Gunners boss Wenger has found himself under fire after Arsenal's failure to win their first two league matches, with his lack of success in the transfer market serving to stoke the fans' frustrations, But a dominant display saw Santi Cazorla open the scoring with an early penalty before Alexis Sanchez and Mesut Ozil increased Arsenal's lead to three by half-time and the imminent arrivals of new signings Lucas Perez and Shkodran Mustafi should give the north London side a further boost.