denigrate vs badmouth

denigrate and badmouth both are verbs.

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

As verbs, badmouth is a hyponym of denigrate; that is, badmouth is a word with a more specific, narrower meaning than denigrate:

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

Other hyponyms of denigrate include assassinate, libel, drag through the mud, malign, traduce.

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