An inquest at Chesterfield Coroners Court heard how six-month-old Hunter Martin died on 6 March 2023 after an infection escalated.
Coroner Peter Nieto told the court there were ‘missed opportunities' to treat Hunter and avoid his death, adding there had been an over administration of antibiotics.
The inquest heard there had been a miscalculation on the dosage of Hunter's antibiotics on five occasions.
In a statement to the court, the trust said Hunter had been given ibuprofen against its guidelines for treating chicken pox, which had "probably masked the early signs of his infection", adding the baby should have had a clinical review and remained under observation longer.
The trust said a diagnosis of Group A Streptococcal infection on Hunter's first admission had been missed. It said the baby would have survived if the infection had been detected and treated with antibiotics.
There were also ‘later missed opportunities to recognise worsening features of sepsis and escalate care to tertiary intensive care', due to the ‘mixed picture of Hunter's observations and clinical status'.
Krishna Kallianpur, executive chief nurse at the trust, said: 'We share our deepest condolences with the family and all those affected by the tragic loss of Hunter.
'We are supporting the inquest process, which will establish the cause of death and make any further recommendations going forward as directed by the coroner.
'We are very grateful to Hunter's family for the work they have undertaken with us on sepsis awareness in children.'
The inquest continues.