Having been put in, Derbyshire were 99 for one after a first day reduced to 31 overs by rain and reached 173 for two by lunch. Paul Borrington was unbeaten on 60 with Shivnarine Chanderpaul on 31.
Nearest challengers Yorkshire made good progress at Hove after bowling Sussex out for 292.
Last man Lewis Hatchett hit 21 before falling to Ryan Sidebottom, who took four for 50, to end the hosts' innings and despite losing Phil Jaques for 21, Yorkshire took lunch on 71 for one with Adam Lyth 31 not out.
Somerset were 108 for four, 87 behind relegation rivals Surrey's first-innings total, despite Nick Compton's unbeaten 57.
Compton lost partner Craig Kieswetter for 32 on the stroke of lunch, ending a partnership of 62.
Nottinghamshire had piled up an impressive 266 for four against Middlesex. Steven Mullaney finally departed for 125 but Samit Patel was unbeaten on 39.
Division Two leaders Lancashire were 146 for one from 40 overs against Leicestershire, having been put in on an opening day restricted to 21 overs.
Paul Horton was 68 not out, with opening partner Luis Reece falling for 50.
Third-placed Essex were battling simply to secure a second batting bonus point after being reduced to 246 for eight by Kent.
Owais Shah added only one to his overnight 83 and Ben Foakes made 58, with captain James Foster still there at the interval on 18.
Hampshire were 277 for six against Worcestershire, with Sean Terry 37 not out and Michael Bates making 41 after James Vince fell for his overnight 106.