Step 1: Meaning of ‘derogatory’.
The word “derogatory” means showing a critical or disrespectful attitude, often used for remarks or comments that insult or lower someone’s reputation.
Step 2: Analyzing options.
- Inflammatory: Means likely to arouse anger, similar in tone but not exact.
- Defamatory: Correct, as it means damaging someone’s reputation, very close to the meaning of derogatory.
- Satisfactory: Opposite in meaning, not correct.
- (Supplementary: Means additional, unrelated.
Step 3: Conclusion.
Thus, the synonym of “derogatory” is “defamatory.”
Final Answer:
\[
\boxed{\text{defamatory}}
\]