Derby took the first step towards easing the pain of their play-off final defeat with a 1-0 victory over Championship newcomers Rotherha
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Fulham's woeful start to the season continued when they were thrashed 5-1 at Derby to pile the pressure on manager Felix Magath.
His young side looked worryingly frail at the back and fell apart as Derby ran riot in the second half with Chris Martin scoring twice.
Jamie Ward gave Derby a half-time lead and although Scott Parker equalised, Martin's double and strikes from Craig Bryson and Simon Dawkins made it a miserable day for relegated Fulham and Magath.
For the second time in three days Jeff Hendrick proved to be Derby's man on the spot, grabbing the second-half goal which broke Carlisle's brave resistance and secured a 2-0 win in the Capital One Cup first-round tie at Brunton Park.
Hendrick, who netted the winner in Derby's Championship opener on Saturday, was unmarked at the far post when he headed in Will Hughes' cross, and Derby secured victory in added time when Chris Martin sidefooted a right-wing cross home from six yards.
Derby head coach Steve McClaren has signed a new three-year contract.
First-team coach Paul Simpson and goalkeeping coach Eric Steele have also extended their deals until 2017.
Derby have signed midfielder George Thorne from West Brom for an undisclosed fee.
The 21-year-old has penned a four-year deal with the Rams having helped them reach the Championship play-off final last season while on loan.
Derby boss Steve McClaren told the club website: "We're really pleased that George Thorne has joined us on a permanent basis.
"I am sure the fans will be delighted to welcome him back and we're equally pleased that he sees Derby County as the right place for him at this point of his career.
"It's taken a lot of hard work for us to get to this stage but I think it says a lot about where we are at as a club that we've been able to bring someone like George in permanently."
West Brom have confirmed they are in discussions with Derby over the possible sale of George Thorne.
Albion are due to fly out to America on Thursday for a pre-season training camp in California, but Thorne will remain in the Midlands while talks between the two clubs take place.
If a deal can not be agreed then the midfielder will link up with the rest of Alan Irvine's squad at a later date.
Derby County: Grant, Wisdom, Forsyth, Thorne, Keogh, Buxton, Hendrick, Hughes, Martin, Russell, Ward.
Subs: Bryson, Eustace, Sammon, Legzdins, Whitbread, Dawkins, Bamford.
QPR: Green, Simpson, Hill, Barton, Onuoha, Dunne, Doyle, O'Neil, Kranjcar, Austin, Hoilett.
Subs: Traore, Morrison, Yun Suk-young, Hughes, Henry, Zamora, Murphy.