Upvote:4
Yes, a residence permit from one Schengen country implicitly gives you the rights to travel within/through the rest of the Schengen area much as if you had a multiple-entry short-stay visa.
You have to comply with the usual 90/180 day rule for days you're in a Schengen country that is not Denmark, but enforcement of this is mostly by the honor system since your passport won't get stamped when traveling between Schengen countries.