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The footage is from an emotional scene in Kate's ITV documentary, Kate Garraway: Finding Derek which airs this evening.
You can watch it below:
In what is an exceptionally emotional time for the couple, Derek can be seen waking up, with Kate saying: "He's back. We've been waiting a long time to speak to you. I'm so proud of you. I'm so proud of you."
Kate appeared on today's Good Morning Britain to discuss the documentary, explaining: "The footage you'll see of Derek was recorded for me personally, that's not been recorded by the documentary crew.
"And it started because after six months we were able to get an iPad into the hospital so I could talk to him in his coma with the idea of trying to bring him out, maybe the voice recognition could help.
"I started recording it because it was so emotional for me to be talking to him, it was all I could do to focus on not falling apart, and giving him a positive energy and not a sad energy.
"And the doctors said, 'are you seeing things that only you might know' and I realised I couldn't examine it forensically, and be emotional. So I started recording it so I could look back on it and think 'oh I said that then, did he react or not react'."
Derek has been in hospital since last March, when he first developed Covid. The disease left him with kidney failure, damage to his liver and pancreas and heart failure.
Doctors have since stopped the drugs that were keeping him in a coma - even causing him to open his eyes - but he remains in a state of minimal consciousness.
A synopsis for the documentary reads: "As Derek, who was hospitalised in March 2020 with the virus, remains in hospital with severe health issues, Kate also meets survivors of the disease and discusses the somewhat unknown, longer-term effects of the virus.
"As Kate lays bare in the film, her family, along with many others who have suffered the effects of the virus, is now facing the reality of adjusting to a very different way of life to the one they lived before the pandemic hit."
The documentary will air tonight on ITV at 9pm.
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