first derivative vs differential

differential vs first derivative

first derivative and differential both are nouns.

first derivative is not an adjective while differential is an adjective.

Word	Noun	Adjective	Verb	Adverb
first derivative	Yes	No	No	No
differential	Yes	Yes	No	No

As nouns, first derivative and differential are synonyms defined as:

first derivative and differential: the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx

Other synonyms of first derivative include derivative, derived function, differential coefficient.

first derivative (noun)	differential (noun)
the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx	a bevel gear that permits rotation of two shafts at different speeds; used on the rear axle of automobiles to allow wheels to rotate at different speeds on curves
	a quality that differentiates between similar things
	the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx

first derivative (adjective)	differential (adjective)
	relating to or showing a difference
	involving or containing one or more derivatives

Difference between first derivative and differential

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