Hit points and multi-classing

[nogoodscallywag]

I have a level 1 Rogue who began with the max 8 HP. When leveling to 2nd level, I choose to add Fighter as a class. Does the additional hit points gained upon taking the new class give me max HP again, or do the rules mean the max is only for the first role of the character, not for the first roll of the class?

For instance, should the rogue now have ROGUE 8hp plus FIGHTER 10hp?

Or, ROGUE 8hp + FIGHTER d10hp?

[Are]

You only get the max hit points for the character's first level, not for every 1st-class-level. So, 8 hp from the Rogue level, then you roll 1d10 to determine the additional hit points from the Fighter level.