misbehave vs act up

misbehave and act up both are verbs.

Word	Noun	Adjective	Verb	Adverb
misbehave	No	No	Yes	No
act up	No	No	Yes	No

As verbs, act up is a hyponym of misbehave; that is, act up is a word with a more specific, narrower meaning than misbehave:

Other hyponyms of misbehave include fall from grace, carry on.

misbehave (verb)	act up (verb)
behave badly	make itself felt as a recurring pain
	misbehave badly; act in a silly or improper way