The Rams picked up their first points of the season before the international break but are still down in 20th place, four points behind opponents Watford.
The Dutchman had seen his side lose their opening three league matches, including a 4-0 reverse at home to Blackburn, before that win in East Anglia.
Throw an early EFL Cup exit at the hands of Preston North End into the equation, and it is fair to say that the pressure had been growing on Cocu.
One victory can change everything in this division, though, and County will now be looking to climb into the top half with victory against Watford.
The Hornets went into the international break on the back of a disappointing 1-0 loss at Reading - George Puscas scoring a first-half winner for the early pacesetters.
That followed an unbeaten three-match start to begin the campaign, with a goalless draw against Sheffield Wednesday sandwiched by 1-0 home wins over Middlesbrough and Luton Town.
Winning away has proved to be an issue for Watford, having picked up just one win in their last 15 away from Vicarage Road, albeit with 13 of those games coming in the Premier League.
This may just be the perfect fixture to end that run, though, as Derby have lost their last four home league games - not since March 2011 have they lost five on the bounce.
Friday's encounter in the East Midlands will be the first between these sides since a 2-2 draw in April 2015.
In their 20 previous away league matches against Derby, Watford have never kept a single clean sheet, shipping 16 goals in their last five such visits.
Derby County Championship form: LLLW
Derby County form (all competitions): WLLLLW
Watford Championship form: WDWL
Watford form (all competitions): WWDLWL
Cocu went with a back five for the win over Norwich, but that was more out of necessity than choice.
Tom Lawrence is back in training after recovering from a shoulder injury and may make his first appearance of the season, though that will likely be from the bench.
Rooney was fielded up top last time out, but Jack Marriott is pushing for a start up top.
The deadline for domestic transfers to go through is shortly before kickoff on Friday, so it could be a stressful day for Hornets boss Vladimir Ivic.
Derby County possible starting lineup:
Marshall; Byrne, Clarke, Davies, Buchanan; Rooney, Bird; Knight, Holmes, Jozwiak; Marriott
Watford possible starting lineup:
Foster; Cathcart, Kabasele, Wilmot; Ngakia, Garner, Capoue, Cleverley, Femenia; Pedro, Sarr
We say: Derby County 1-1 Watford
Derby have a poor record on home soil, while Watford struggle to pick up wins away from home, suggesting that this one should finish in a draw.