Paul Borrington (17 not out) and Billy Godleman (18 not out) were unbeaten at the break after stitching an unseparated 30-run partnership for the third wicket.
Pace spearhead Bhuvneshwar Kumar and all-rounder Stuart Binny were rewarded for their consistent bowling. Kumar drew first blood after scalping opener Ben Slater for nought.
Sharing the new ball, Mohammad Shami (0-23) also seemed to get his act right as the two bowled incisive spells at the top, particularly Kumar, who seems to have gotten on top of his problems post the first game in Leicestershire.
Binny continued his fine work-out in this game, picking the wicket of skipper Chesney Hughes (20). It goes well with his spell of 1-25 in the first innings on day one as well as his half-century yesterday. Ravindra Jadeja (0-7) and Murali Vijay (0-8) too sent down some overs of spin.
On day one, Derbyshire had won the toss and thanks to half centuries from Wes Durston (95), Ben Slater (54) and Harvey Hossein (53 not out) piled up the runs against the Indian attack. Ravindra Jadeja (2-27), Pankaj Singh (1-63), Ishwar Pandey (1-34) and Stuart Binny (1-25) were the wicket-takers for the visitors.