Are a Level 1 Druid's cantrips changeable each day?
(As opposed to picking 2 cantrips at the start of Level 1, and those are the ones you keep until until you get more at higher levels.)
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Cantrips are not prepared like the rest of your leveled spells. From the Druid Spellcasting class feature section:
At 1st level, you know two cantrips of your choice from the druid spell list. You learn additional druid cantrips of your choice at higher levels, as shown in the Cantrips Known column of the Druid table.
Preparing and Casting Spells
...You prepare the list of druid spells that are available for you to cast, choosing from the druid spell list. When you do so, choose a number of druid spells equal to your Wisdom modifier + your druid level (minimum of one spell). The spells must be of a level for which you have spell slots...
A cantrip is a spell that can be cast at will, without using a spell slot and without being prepared in advance. Repeated practice has fixed the spell in the caster's mind and infused the caster with the magic needed to produce the effect over and over. A cantrip's spell level is 0.
Since the cantrips are not prepared and you learn them as you level you cannot change them out when you prepare spells.
It is important to note that you do retain all of the cantrips you learn as you level, new cantrips such as when you choose your circle do not replace your previously known cantrips.
No, cantrips are not changeable each day. When a Druid prepares the day's spells, the spells "must be of a level for which you have spell slots" (PHB, Druid, Preparing and Casting Spells, p.66), and there are no spell slots listed in the Druid's class table for cantrips/0-level spells, so cantrips can't be set on a daily basis.