The 4-0 victory against promoted Bolton on August 25 followed successive Sky Bet Championship defeats to Wolves and QPR and a Carabao Cup exit at the hands of Doncaster.
Seven Hull players departed to represent their countries after the much-needed win over Bolton, and now Slutsky wants the reunited squad to perform purposefully when they head to Pride Park on Friday.
He said: “We played well against Bolton last time out, but I hope we will play each match better and better.
“Derby are strong and experienced. They are a very good team and all players are experienced. But like every team, they have strengths and they have weaknesses – we will try to use their weaknesses.”
Slutsky confirmed all of his new signings could be available, with Markus Henriksen back fit, and Fraizer Campbell, Evandro and Ondrej Mazuch being examined in training.
Derby fared differently against promoted opponents, as they finished before the break with a 3-1 loss to League One’s runaway 2016/17 champions Sheffield United.
Manager Gary Rowett suggested changes would be made after Derby’s defeat and said he will hand summer signing Tom Lawrence, fresh from World Cup qualifying duty with Wales, his first start. Lawrence, who joined Derby from Leicester, had a successful loan spell at Ipswich last season.
Rowett told Rams TV: “He was a key signing for us during the summer and he brings goals to the side, so we want to see him.
“What better way to see him than on Friday night at home against Hull?
“He will be desperate to get out there and impress following his international exploits with Wales. We will see if he can add something different to the team.
“Myself and the fans, I am sure, will look forward to seeing him play.”
Rowett also confirmed the transfer of Birmingham midfielder Maikel Kieftenbeld to Derby has not been authorised by the EFL, and the player has returned to the West Midlands.