The chain by which one thing came from another. A derivation is what makes a result checkable rather than merely asserted.
Latin derivatio (a diverting, drawing off), from derivare (to divert a stream), from de- (away, from) + rivus (a stream); the chain by which one thing was drawn off from another, tracing a path a claim can be checked against.
The Latin image is a channel cut from a river, not an assertion made from nothing — a derivation is a path a claim travelled, and the path can be walked back. What has no such channel has to be taken on trust instead.