Mark Turner picked up three wickets, including two with successive deliveries, on a hard day in the field for Derbyshire, as Somerset closed on 470-5 at Taunton.
Both Marcus Trescothick (106) and James Hildreth (182) reached three figures for the hosts who ended the second day with a 241-run lead.
Turner was the pick of the bowlers with three wickets while David Wainwright and Ross Whiteley both claimed a wicket apiece.
Somerset resumed their first innings on 83 without loss, in reply to Derbyshire’s 229 all out, with both Trescothick and Arul Suppiah getting starts on the first day.
Trescothick soon completed his 50 in 71 balls, but Suppiah would fall five short of his half-century when he was caught by Wes Durston at first slip off Mark Turner with the score on 117. The paceman would collect his second wicket with the very next delivery bowling England’s Craig Kieswetter to reduce Somerset to 117-2.
New man James Hildreth joined his Captain at the crease and the pair moved the scores onto 179-2 at lunch on day two.
Somerset moved past 200 after the restart as Trescothick completed his century from 162 deliveries, before he finally fell for 106 as he was caught at slip off David Wainwright as the scores moved to 212-3.
Hildreth brought up his half-century shortly after as he and new batsman Jos Buttler began to build a first innings lead for the hosts. At tea, Hildreth had followed his Captain to three-figures and stood unbeaten on 118 while Buttler was 38 not out with the scores on 325-3.
Turner claimed his third wicket of the day shortly after the restart as Jos Buttler was caught by Chesney Hughes for 38.
Hildreth had looked set for the rest of the day, but on 182 he edged Ross Whiteley through to wicketkeeper Richard Johnson with the total on 442.
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