At lunch the visitors had advanced their first innings score to 177 for three, with the two experienced batsmen having added 112 together before Madsen fell just before lunch.
By the interval, Godleman was undefeated on 75, with Alex Hughes on six not out, as Derbyshire had reduced their deficit to just 52.
Resuming from their overnight 52 for two, Derbyshire enjoyed the better of the early exchanges with Nottinghamshire’s bowlers not quite at their best.
Madsen, who began his innings today after Shiv Thakor had fallen in the final over of yesterday’s play, was able to get his innings up and running by tickling Harry Gurney to the leg side fence for four and then repeated the dose off Luke Fletcher.
Godleman, the visiting skipper, reached his 50 from 80 balls with six fours and his partner brought up the same milestone from 94 deliveries with nine fours.
With 20 minutes of the session remaining Brett Hutton enabled Notts to gain their first bowling point by pinning Madsen lbw for 56.