13-year-old Duwayne Philpott and his seven brothers and sisters were asleep upstairs in their Victory Road home when the blaze began.
The fire is being treated as suspicious by police.
A man of 38 and a woman of 28 were both arrested, and have now been released on bail, on suspicion of murder.
The family’s father Mick Philpott is well known in the Derby areas, as he is reportedly the father of seventeen. Eight of his children lived in the Victory Road house, and he is believed to have made “valiant attempts” to save his children from the blaze.
Five children died in the fire on Friday, while Duwayne was being treated at Birmingham Children’s Hospital, before his life support machine was switched off. Mr Philpott and his wife were at the child’s bedside when he passed away.
The hospital said in a press statement, "Despite the intensive care team's greatest efforts, the injuries that Duwayne received in the fire were too great for him to survive.
"Our thoughts are with his family at this difficult time."
Meanwhile, police in Derby have called for anyone with information on how the fire started to come forward. They would like to speak to anyone who was on Victory Road between 0300 and 0400 on Friday morning.
Assistant Chief Constable Steve Cotterill said, "I want to thank the local community who have already come forward but I would urge anyone with any information, regardless of how insignificant you think it may be, to contact us.
"My deepest sympathies go out to Mr and Mrs Philpott at this distressing time."