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Mathematics-Online lexicon:

Derivative

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A function is differentiable at the point if the limit

exists. This limit is called the derivative of at .

Geometrically, differentiability means that the slopes of the secants converge to the slope of the tangent given by

We also write

with . This notation symbolizes the limit for the difference quotient.

Higher derivatives are denoted by or , respectively.

We say that a function is differentiable on a set if exists for all .