Good luck with your Derby
This is the most erratic watch ever invented and I currently hate it as much as I love it.
I have repaired dozens of these and neither of them are alike although many share similar issues.
Play with the stud regulator on the balance hairspring which is the basic adjustment for any mechanical watch.
If the issue is elsewhere it will be mechanical friction due to age/wear on the plastic gears or rarely a capacitor out of specs on the battery clamp.