To obtain one thing from another by a traceable path. Derivation is what makes a result checkable.
Latin derivare (to divert a stream, draw off), from de- (away, from) + rivus (a stream); to obtain one thing from another along a traceable path, the way a channel is drawn off from a river.
It is derivation's own verb, the drawing-off itself rather than the channel left behind by it — Latin rivus, a stream, diverted rather than dammed. What is derived can always be traced back upstream to what it was diverted from.