Emergency services were called to the incident, which involved one car, on Saturday, April 23, at about 2.15am.
The car, a silver Ford Focus, was travelling on the southbound carriageway of the A38, near to the exit for the B600 at Somercotes, when it left the road and collided with a tree.
Two women and a man died at the scene.
Derbyshire Police said their families are aware and are being supported by specially trained officers and that their thoughts are with them ‘at this most distressing of times’.
A man and a woman remain in hospital, with the man being described as in a critical condition and the woman in a stable condition.
Anyone who witnessed the crash or noticed the car, which had been travelling southbound on the M1 before the collision, is asked to contact Derbyshire Police.
The force are also appealing for anyone with dashcam or CCTV footage which could help with their enquiries to get in touch.
If you have any information which you think could help, call Derbyshire Police on 101 quoting reference 22*0229425.
To report information anonymously, contact the independent charity Crimestoppers on 0800 555111 or visit crimestoppers-uk.org