Liam Whoriskey of Glenabbey Gardens in the city, denies the manslaughter of the toddler in 2017.
The three year old was found dead in his bed in his family flat at Colmcille Court in the Bogside area on Sunday, September 17, around 10 am.
The defendant also denies one count of child cruelty on 15 August 2017.
The BBC reports that at Derry Crown Court, the jury of six men and five women were told by the judge to put sympathy and prejudice out of their minds and judge the case on the facts alone.
Judge Philip Babington told the jurors that the trial had been a very emotional case for all involved.
He told the jury that he did not pretend that the task before them was easy but he said he had every faith in the ability of the jurors to discharge their responsibilities properly.
They alone were the judges of the facts, Judge Babington said.
Judge Babington told the jurors they must consider the two charges separately and that they were entitled to come to common sense conclusions.
He said the burden of proof was on the prosecution and the defendant did not have to prove his innocence.
The trial had started as a murder case but on last Friday the new charge of manslaughter was added to the bill of indictment.
Whoriskey denied the charge.
During his evidence he told the jury he did not kill or assault Kayden.