derive vs extrapolate

derive and extrapolate both are verbs.

Word	Noun	Adjective	Verb	Adverb
derive	No	No	Yes	No
extrapolate	No	No	Yes	No

As verbs, extrapolate is a hyponym of derive; that is, extrapolate is a word with a more specific, narrower meaning than derive:

derive: reason by deduction; establish by deduction
extrapolate: gain knowledge of (an area not known or experienced) by extrapolating

Other hyponyms of derive include surmise, elicit.

derive (verb)	extrapolate (verb)
develop or evolve from a latent or potential state	estimate the value of something based on known values
obtain from a particular source	gain knowledge of (an area not known or experienced) by extrapolating
reason by deduction; establish by deduction	draw from specific cases for more general cases
obtain
come from; be connected by a relationship of blood, for example