Answer
The answer is no, Matt Derbyshire has never played for Arsenal in the Premier League. He started his career at Blackburn Rovers, where he made 41 appearances and scored 10 goals. After leaving Blackburn, he had loan spells at Plymouth Argyle and Olympiacos, before joining Nottingham Forest in 2008. He later played for Birmingham City, Cardiff City, and Bolton Wanderers, among other clubs, but never represented Arsenal.