verb (used with object), differentiated, differentiating.
to form or mark differently from other such things; distinguish.
to change; alter.
to perceive the difference in or between.
to make different by modification, as a biological species.
Mathematics. to obtain the differential or the derivative of.
verb (used without object), differentiated, differentiating.
to become unlike or dissimilar; change in character.
to make a distinction.
Biology. (of cells or tissues) to change from relatively generalized to specialized kinds, during development.

1810–20; < Medieval Latin differentiātus distinguished (past participle of differentiāre), equivalent to Latin different(ia) difference + -ātus -ate1

differentiation, noun
interdifferentiate, verb (used with object), interdifferentiated, interdifferentiating.
redifferentiate, verb, redifferentiated, redifferentiating.
self-differentiating, adjective
undifferentiated, adjective

1. set off. See distinguish. 3. separate.
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
differentiate (ˌdɪfəˈrɛnʃɪˌeɪt)
vb (when intr, often foll by between)
1.  (tr) to serve to distinguish between
2.  to perceive, show, or make a difference (in or between); discriminate
3.  (intr) to become dissimilar or distinct
4.  maths to perform a differentiation on (a quantity, expression, etc)
5.  (intr) (of unspecialized cells, etc) to change during development to more specialized forms

Collins English Dictionary - Complete & Unabridged 10th Edition
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Word Origin & History

1816, formed from different on model of Fr. différencier. Originally a mathematical term, trans. and non-technical sense of "discriminate between" is from 1876. Earlier, difference had been used as a verb in this sense. Related: Differentiated; differentiating; differentiation.
Online Etymology Dictionary, © 2010 Douglas Harper
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Example sentences
The only thing that differentiated humans from animals was that they had the
  ability to speak, think, and reason.
Some comments have talked about motion but not differentiated between linear
  and circular motion.
The authors suggest that the five models can be differentiated through
The system hinges on the ability to use a differentiated enough pattern so each
  gesture can be looked up quickly in a database.
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