The quality or state of being derogatory; the characteristic of showing disrespect or being disparaging.
From 'derogatory' + '-ness' suffix creating an abstract noun. This nominalizes the adjective to express the quality itself as a noun.
This noun is so theoretically constructed that it's rarely used in real conversation—but it represents how English can nominalize almost any quality. The 'derogatoriness' of a comment is its capacity to insult, compressed into a single noun.
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