Root was the star performer in the White Rose's win at Durham with an innings of 182 on Saturday and he was again proving his worth with an unbeaten 130 off 191 balls.
That led Yorkshire to 251 for three - still 224 runs behind Derbyshire's first-innings total - although they seem well-placed to avoid the follow-on.
Durham have eked out a first-innings lead against Nottinghamshire at Trent Bridge, largely thanks to the efforts of Will Smith.
The opener has come in for some criticism after an indifferent start to the season but his 153 carried Durham to 364 for eight and a lead of 44. Smith's resistance was finally ended on Wednesday morning when he fell to slow left-armer Samit Patel.
Stuart Broad claimed his third scalp when overnight batsman Phil Mustard was caught behind, but fellow England bowler Graeme Swann remains wicketless from 31 overs.
Defending champions Warwickshire won the toss and went to lunch on day one of their clash with Sussex on 83 for one at Hove.
Varun Chopra, who contributed a century as the Bears valiantly held Somerset to a draw last week, was unbeaten on 46, while Ian Bell captains the side which also includes England team-mate Jonathan Trott in the absence of the injured Jim Troughton.