Billy Godleman (67 not out of 159 balls, 8x4s) and 17-year-old Harvey Hossein (53 not out of 89 balls, 8x4s) were at the crease at the end of opening day's play.
The only bright spark for the visitors was the first hour of the lunch session when Ravindra Jadeja (2/27) and Ishwar Pandey (1/34) bowled well in tandem to pick up three quick wickets.
Jadeja only bowled one spell in the middle session and that was when Indian looked in control. But on either side of his spell, Derbyshire batsmen made merry while the sun shone bright all day, accumulating runs at ease. In the post-tea session, the hosts scored 140 runs in 34 overs.
It didn't bring about any more breakthroughs as Godleman constructed another fine partnership, this time adding 87 runs with Hossein, as he brought up his fifty in the 74th over of the day.
Bhuvneshwar Kumar (0/24), Pankaj Singh (1/63), Varun Aaron (0/45), Ishant Sharma (0/49) and Ishwar Pandey (1-34) bowled second spells in the post-tea session.