Priscialla Owusu, 21, was driving a silver Ford Focus along the southbound carriageway at around 2.15am on Saturday, April 23.
She was close to the exit for the B600 at Somercotes when the car left the road and collided with a tree.
She was pronounced dead at the scene of the crash, along with front seat passenger Rebecca Donkor, also 21. Both women were from Derby.
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A third person, who was sat in the back of the car, also died in the collision – he was previously named as Kudakwashe Mdianyama, 23, from Coventry.
A Derbyshire Police spokesperson said: “Our thoughts go out to their families and friends at this sad time.”