Does Rage Prevent Divine Smite?

Question

I was reading both of them, and if you had a hypothetical Barbarian Paladin multiclass, would the use of divine smite be prevented by raging? Unlike other smites, it says that it expends a spell slot, but isn't listed necessarily as a spell. It reads more like a special ability that just happens to cost a spell slot.

Divine Smite:

Starting at 2nd level, when you hit a creature with a melee weapon attack, you can expend one spell slot to deal radiant damage to the target, in addition to the weapon’s damage. The extra damage is 2d8 for a 1st-level spell slot, plus 1d8 for each spell level higher than 1st, to a maximum of 5d8. The damage increases by 1d8 if the target is an undead or a fiend.

Rage: (Relevant portion)

...If you are able to cast spells, you can’t cast them or concentrate on them while raging.

Answer 1

You can smite divinely while enraged.

There's no spell named divine smite; you're not casting a spell when you use that class feature. It's a feature triggered when you hit with a weapon attack.

This, by the way, is another way you know it's not casting a spell: you're (most-likely) taking the Attack action to make your melee weapon attack, rather than the Cast A Spell action. It's rare--and explicitly spelled-out circumstances--where you'd make an attack but end up casting a spell.

Answer 2

No, raging does not prevent you from using Divine Smite. As you said, it is a special ability that just happens to use a spell slot. If it was intended to be a spell, it would have to call it out as such.

As it is, you simply expend one spell slot and some other effect happens. Just because it is similar to casting a spell in process does not mean that it is a spell, and therefore you can use it while raging.