Electing to bat first, Derbyshire, who are second from bottom in the Division 2 County Championship table, scored 79 for two in 25.4 overs at the stroke of lunch.
Skipper Chesney Hughes was bowled just ahead of lunch, after scoring 23 runs (60 balls, 4 fours), while Ben Slater (39*, 82 balls, 6 fours) was the unbeaten batsman.
Like the game in Leicester, this match too hasn't been accorded First-Class status since the visitors have chosen to field all their 18 players over the next three days. Derbyshire will also get to choose from 12 nominated players.
Singh (1-21) was the pick of the Indian bowlers in the morning session, impressing once again with his line and length as well as the bounce he was able to generate during the eight overs he bowled.
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Varun Aaron, who came in as the first change bowler, continued to work up good pace but wasn't as consistent with his line as Bhuvi or Singh. Though he got better with each passing delivery and returned with figures of 0-10 from his four overs.
The lanky pacer bowled four no-balls in four overs and was taken for five runs per over, never looking in control to trouble the batsmen or stop the runs.
It was a worrying sight as the batsmen saw off the early spells and scored runs at brisk pace. The 50-run mark came in the 18th over, with Hughes and Slater putting on 70 runs for the second wicket.
The left-handed Slater was bowled by Ravindra Jadeja (1-0) at the stroke of lunch.