IPA: /dɪˈrɒɡəˌtɔːri/
KK: /dɪˈrɑɡəˌtɔri/
Showing a negative or disrespectful attitude towards someone or something; often used to describe comments or remarks that belittle or insult.
He made a derogatory remark about her appearance that upset her.
Derogatory is formed from "derogare" (meaning to detract or take away) and the suffix "-ory" (meaning relating to or characterized by). The word describes something that is characterized by detracting from someone's worth or reputation.
Think of something that 'takes away' ('derogare') from someone's value — that's why derogatory means something that belittles or insults.