As an adjective, it means not original, copied or developed from something else. In math and finance as a noun, it refers to a quantity or product that is based on or comes from another thing, like a function’s rate of change or a financial contract based on an underlying asset.
From Latin *derivare* meaning 'to lead or draw off (water)', from *de-* ('from') and *rivus* ('stream'). The noun form developed to mean something that has been 'drawn off' or taken from a source.
In everyday speech, 'derivative' is a criticism—your idea is just a copy. In calculus, it’s a powerful tool that tells you how something is changing at every instant, literally 'drawn off' from the original function.
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