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Let f be a function and a be the given point you are considering. Then,


f(x) - f(a)
---------------
(x-a)


is the difference quotient. If the limit as x approaches a exists, then the function is differentiable at a, or we say the derivative exists at a. If that limit does not exist, then the derivative does not exist at that point.

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Q: When does the derivative of a function exist at a given point?
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