Hendrie, son of former Middlesbrough and Bradford forward John Hendrie, is without a club after he was released by the Premier League champions at the end of last season.
The teenage midfielder played 70 minutes for the Rams' development squad against Crewe on Monday afternoon.
Another trialist midfielder - former Tottenham youngster Dean Parrett - also featured, playing the whole match as Derby were beaten 2-1.
Michael Jacobs scored Derby's goal and he had the chance to earn his side a draw with an injury-time penalty but his spot-kick was saved by the Crewe goalkeeper.
- Sports & Recreation
- John Hendrie
- Dean Parrett