Expressing a low or poor opinion of someone or something.
Example:
The radio talk-show host tried to discredit the politician by making derogatory remarks about his appearance.
Derogatory also comes from the "propose" sense of rogare. When Romans wanted to propose that something be taken out of a law, the verb they used was derogare, and this word developed the general meaning of "take away from." A derogatory comment is one that takes away because it detracts from a person's reputation or lowers the person in the eyes of others. Derogatory remarks are a specialty of some comedians, though their meanness sometimes detracts from their humor.