Somerset seamers Jamie Overton and Alfonso Thomas each claimed three wickets as Derbyshire were dismissed for 266 on day one.
Teenager Overton finished with 3-35 and veteran South Africa Thomas 3-54 before Somerset reached 16-0 in reply at stumps in the Division One basement battle.
Somerset skipper Marcus Trescothick won the toss and sent in hosts Derbyshire under heavy cloud cover at the County Ground.
Overton had Billy Godleman (5) held by Trescothick at slip in the sixth over before Chesney Hughes (25) and Wayne Madsen put on a 52-run stand.
From 67-1, Derbyshire collapsed to 173-7 with Steve Kirby (2-61) removing Madsen for a 108-ball 50 featuring eight fours.
Derbyshire's lower order, led by wicketkeeper Richard Johnson's 56 and 49 from Tony Palladino, rallied to ensure their side at least picked up a couple of batting bonus points.
Overton polished off the innings late in the day with wickets in successive overs, leaving Somerset openers Trescothick and Nick Compton to survive seven overs to stumps.
Compton was missed on two when a mistimed hook at Mark Footitt's left-arm seam was put down by Ben Slater diving at leg gully, but there were no further alarms.
Derbyshire and Somerset occupy the relegation spots in the Division One and neither side has yet won a County Championship game this season.