badmouth vs denigrate

badmouth and denigrate both are verbs.

Word	Noun	Adjective	Verb	Adverb
badmouth	No	No	Yes	No
denigrate	No	No	Yes	No

As verbs, denigrate is a hypernym of badmouth; that is, denigrate is a word with a broader meaning than badmouth:

badmouth: speak unfavorably about
denigrate: charge falsely or with malicious intent; attack the good name and reputation of someone

Other hypernyms of badmouth include asperse, besmirch, calumniate, defame, slander, smear, smirch, sully.

badmouth (verb)	denigrate (verb)
speak unfavorably about	cause to seem less serious; play down
	charge falsely or with malicious intent; attack the good name and reputation of someone