A silver Audi careered across the road and ploughed into railings at Culmore Primary School shortly before 10 am on Thursday.
Police quickly arrested Six people in connection with the crash.
They have all bave been released pending further police enquiries.
Principal of Culmore Primary Clare McMenamin said the incident could have ended in tragedy.
“Thankfully, the children coming to our school no longer use the front entrance. They use a car park and side entrance, so they were not at risk,” she told the Belfast Telegraph.
“That doesn’t take away from what those joyriders did, which was horrendous, because there were other children waiting to go to a school around the corner from us on that footpath an hour before this crash happened.
“In fact, it was a miracle no one was injured, because there were other pedestrians walking along the path at the time.
“Had this been an hour earlier, there is no doubt schoolchildren going to other primary, secondary and grammar schools were in danger because children – my own children included – would have been at bus stops along the road.
“It makes my blood run cold when I think about what could have happened. It was a complete disregard for human life.”
Sinn Fein councillor Sandra Duffy said she was horrified by the incident.
“Once again, we see the total disregard these death drivers have for the lives of other people. That this happened before 10am just beggars belief,” she said.
“Realistically, the people in this car could have lost control at any time and there is not a shadow of a doubt in my mind that we could easily have had a terrible tragedy.
“I have spoken to the police about the whole issue of death drivers in Derry and the people who are selling them these runarounds.”
Police have appealed to anyone who was in the Culmore Road area on Thursday morning at around 9.45am to call them on the non-emergency 101 number.
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