A lot depends on the caliber of the derringer and when your story is set. In modern day it almost surely would penetrate the skull. A small caliber round like a .22 would make a small hole going in then bounce around inside the skull, scrambling the victim's brains.
A larger round like a .38 or bigger would make a large hole going in (obviously) and blow the back of the guy's head off coming out. In either case there might be a trickle of blood from the forehead wound but no more since the heart would stop almost immediately.
In olden days, muzzle velocity was lower but bullets were larger and tended to tumble. So they would smash a larger area of the skull when they hit, meaning a larger hole if they penetrated. There would be more blood than with a modern round because death would not be instantaneous. If the bullet only slammed into the skull without penetrating, there probably would lots more blood since the scalp is one of the most heavily veined areas of the body.
Aside here: most deaths in the Civil War (and before) were not from bullets but from infection to the wounded area.
Hope this helps.