Frank Lampard's Derby started their pre-season with a 4-1 victory over Notts County on Saturday.
Luke Thomas, 19, opened the scoring after just two minutes before adding his second before the break.
Mason Bennett made it 3-0 in the second half and Tom Huddlestone rounded off the scoring after Kane Hemmings pulled a goal back from the penalty spot.
Andriy Yarmolenko made his West Ham debut in a 1-0 friendly win over Wycombe.
Yarmolenko, who signed from Borussia Dortmund on Wednesday, started the match along with Marko Arnautovic, who scored the winner after 34 minutes.
Brighton started their pre-season with a 1-1 draw against St Gallen.
The Seagulls were without new signings Jason Steele and Florin Andone as well as World Cup trio Mat Ryan, Jose Izquierdo and Leon Balogun.
Tomer Hemed's second-half header earned the Seagulls a draw.
Bournemouth also played out a 1-1 draw with La Liga side Sevilla.
Summer signing David Brooks started for the Cherries, who saw Jordon Ibe score in the second half to cancel out Ben Yedder's opener.
Wolves won the Uhrencup with a 4-0 victory over Swiss champions BSC Young Boys.
Ivan Cavaleiro, Helder Costa, Leo Bonatini and Rafa Mir scored the goals in Bern.
Huddersfield lost 3-0 to League Two champions Accrington Stanley while Reading and Fulham drew 0-0.
Maxime Le Marchand made his debut for Fulham while fellow new signing Jean Michael Seri watched on.
West Brom were 3-1 winners against Swindon thanks to goals from Jay Rodriguez, Kyle Edwards and Kyle Jameson.
Bojan and Ibrahim Afellay scored inside the opening five minutes as Stoke won 3-0 against Walsall.
Peter Crouch also got on the scoresheet after the break.
Adam Le Fondre and Sammy Ameobi scored to give Bolton a 2-1 win over Halifax.
Clayton Donaldson, Jason Lowe and Erhun Oztumer made their debuts for Bolton.
Patrick Bamford scored the only goal of the game as Middlesbrough won 1-0 against Sandhausen.