Derby played well in periods but the brutal truth is that they were torn apart by the movement and passing of Arsene Wenger's team who could and should have scored more.
It is no exaggeration to say that Arsenal might have broken the double figure barrier, although an Emmanuel Adebayor hat-trick still highlighted the yawning gulf between the sides.
At least the Rams will not have to face the striker next season and for that they will be greatly relieved. This was Adebayor's second hat-trick against Derby this season and both Nicklas Bendtner and Robin van Persie might also have staked a claim to the match ball.
Derby boss Paul Jewell said before the game that Arsenal were the best team in the country to watch, but this must have been painful viewing from the home dug-out as the speed of the Gunners' attacks ripped the home defence apart with alarming ease.
And yet Derby had matched the visitors for the first opening 25 minutes and drew level before Arsenal engaged the turbo after the interval.
Bendtner put his team in front in the 25th minute after awful defending allowed the Dane to play a one-two with van Persie before driving a low shot inside the right-hand post.
Van Persie should have almost immediately made it two but fired wide from 12 yards and, three minutes later, Derby levelled when Robbie Savage's free-kick bounced off Jay McEveley's shoulder before the defender reacted by stabbing the loose ball in from eight yards.
Roy Carroll kept Derby afloat until the 40th minute when Kolo Toure chipped the ball over Darren Moore and this time van Persie chested it down and fired into the top left-hand corner.
From then on, Arsenal pulled Derby apart and only Carroll kept the score down until the Rams defence collapsed in the closing 11 minutes.
Adebayor replaced van Persie for the second half and scored the third goal in the 59th minute when the hugely impressive Denilson played in Theo Walcott whose low cross was touched in at the far post.
Walcott should have scored before Rob Earnshaw, Derby's record £3.5million signing, scored his first goal for the club in the 77th minute when Andy Todd sent him clear.
But that only roused Arsenal to greater heights and, two minutes later, Walcott got in on the right to curl a shot inside Carroll's left post.
Adebayor slid in for his second when Gael Clichy crossed from the left and the rout was completed in stoppage time when the Togo international raced clear to sidestep Carroll and roll the ball into an empty net.
Derby have now conceded six goals in each of their last two home games and have let in 11 against Arsenal this season. The good news is that there are only two Premier League games left.