Nottinghamshire 256 for 7 (Duckett 69*, Hameed 57, Hudson-Prentice 4-50) lead Derbyshire 149 (Fletcher 3-36) by 107 runs
Nottinghamshire, looking to book their place in the top division in the concluding phase of the LV= Insurance County Championship, will take a lead of 107 runs into day three against Derbyshire at Trent Bridge.
Haseeb Hameed made 57 and Ben Duckett is unbeaten on 69, although Derbyshire's pace-bowling allrounder Fynn Hudson-Prentice checked Nottinghamshire's progress with 4 for 50 as the home county closed on 256 for 7.
Earlier, from 91 for 5 overnight, Derbyshire subsided to 149 all out in the morning session, Luke Fletcher taking 3 for 36.
Derbyshire's last five wickets fell for 32 after the partnership between Hudson-Prentice and Leus du Plooy that began on Sunday was ended just inside the first hour when the former drove Dane Paterson straight to cover.
With five fours, Hudson-Prentice had been the only Derbyshire batsman to hint at assertiveness against an attack that delivered 36 maidens, 10 each from Fletcher and Brett Hutton, nine in 15 overs from Paterson.
Du Plooy fell without addition to the total, having faced 141 balls for his 30, drawn into chasing a wide delivery from Fletcher. Paterson removed Alex Thomson leg before, Michael Cohen - dropped on nought - drove airily at Hutton to be caught behind, and Ben Aitchison found the fielder on the square-leg boundary.
Two wickets in two balls from Hudson-Prentice had Nottinghamshire 25 for 2 as Ben Slater miscued to mid-on and Ben Compton edged to third slip. But Hameed and Steven Mullaney fashioned a measured recovery to 94 for 2 at tea with six fours apiece, Hameed driving handsomely through the off side, Mullaney profiting mainly from cuts and pulls.
Hudson-Prentice removed both soon after tea, Mullaney wafting at a short ball outside off to be caught at first slip after a stand of 78, Hameed passing fifty for the fifth time this season but then tickling a thin edge through to keeper Harvey Hosein.
Duckett helped Lyndon James add a rapid 61 in 13 overs to give Nottinghamshire the lead but one wicket again brought another. James flashed at one from Cohen to be caught at second slip before Aitchison juggled and then held a chance at first slip as Liam Patterson-White departed in a double-wicket maiden for the left-arm quick.
Joey Evison was caught behind as Aitchison claimed Derbyshire's seventh wicket but Duckett timed the ball nicely and his 10 boundaries enabled Nottinghamshire to claim a second batting bonus point in a marathon final session of a 104-over day following Sunday's rain.