der

The root der comes from Latin dērīvāre, 'to lead or draw water off from a source.' Take it apart: dē- ('from, away') + rīvus ('a stream, a brook' — the same rīvus we still hear in river and rival). A dērīvātiō was literally a channel cut to lead water away from a main stream. So the original picture is wonderfully concrete: you tap a river and guide some of its water along a new course.

From that water-channel image English gets a small but important family, all about something coming from a source:

- derive: to draw or trace something from its origin. We derive a word from Latin, derive energy from the sun, derive pleasure from music — in each case something flows out of a source, like water from a stream.
- derivation: the act of deriving, or the source itself — especially the etymology of a word ('the derivation of 'salary' is the Latin for salt').
- derivative: something drawn from something else. As an adjective it often turns critical — a 'derivative' film is one that merely copies others, with no fresh source of its own.

The metaphor survives most beautifully in mathematics. A derivative measures how one quantity changes in relation to another — it is, quite precisely, a value drawn off from an original function. And in finance, a derivative (an option, a future) is an instrument whose value is drawn from some underlying asset. Across language, math and money, the same Latin picture holds: a value led off from a source, like water channeled away from a stream.

A warning about look-alikes: the letters d-e-r sit inside many English words by pure accident — gender, ladder, wonder, consider. None of these come from dērīvāre. The der family is small and tightly bound to the idea of drawing from a source; if a word isn't about origin or flowing-from, the 'der' in it is a coincidence.