Argyle
If asking such questions best to state the exact date of death to save people searching, I had posted the death cert link so could just open, otherwise it is not in the thread.
It did not become commonplace for all to place a death notice until 1940's, yes there are some and they became more commonplace as time progressed, but in 1906 tend to be prominant people or families that had spare cash to pay for one. Similarly do not expect to find a headstone for all in that era, the burial may not even have been in a private purchased plot. Especially from a widow with 7 children whose husband could not afford the mortgage payments in Feb of that year & who would now have to seek work.
Even later the likes of the Belfast Telegraph or Newsletter were more popular places for death notices throughout N.I as they were published daily Mon-Sat. Regional papers were sometimes just published once or twice a week. Burials were typically 2 days after death so if put in the local paper would not appear till after the internment.
The Londonderry Sentinal was published on Tues and Sat in the morning & The Derry Journal on Wed, Sat & Mon.
David died on Sat 25th Aug, there is no death notice in the Sentinal or Journal on Mon 27th (or 25th).
Hope you have managed to read one or other of the Jan 1909 articles using the 3 free views available on
https://www.britishnewspaperarchive.co.uk/account/register utilising the advanced search to narrow results to County, newspaper, exact date & name. Alternatively a sub for a month is £12.95.
Other newspaper articles with David Simpson are Derry Journal 24 February 1892 platform porter Northern Counties Railway during a inquest held Dungiven Road area of Waterside into the death of a signal man who fell from his signal box.
Some in the 1880's for being drunk and one for a David Simpson boy fighting Spencer Road Waterside Derry Journal 9 May 1879.
David, Robert & Samuel Simpson Torry's Rd, Waterside for drunken row Londonderry Sentinel 30 June 1888.
Derry Journal 30 December 1898 David Simpson of Violet St Waterside summoned his brothers Samuel & William of Moore St for stealing & taking away a game cock on Xmas day for fighting, he paid mother for feeding. David moved to Violet St 19 Sep, previously in Moore St with his mother; was working for Northern Counties Railway. All interviewed, including mother who said bird was hers. Dismissed.