extrapolate vs derive

extrapolate and derive both are verbs.

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

As verbs, derive is a hypernym of extrapolate; that is, derive is a word with a broader meaning than extrapolate:

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

Other hypernyms of extrapolate include deduce, deduct, infer.

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