Definition:Derivative/Real Function/Derivative at Point/Definition 1
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Definition
Let $I$ be an open real interval.
Let $f: I \to \R$ be a real function defined on $I$.
Let $\xi \in I$ be a point in $I$.
Let $f$ be differentiable at the point $\xi$.
That is, suppose the limit $\ds \lim_{x \mathop \to \xi} \frac {\map f x - \map f \xi} {x - \xi}$ exists.
Then this limit is called the derivative of $f$ at the point $\xi$.
Also see
Sources
- 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 10.1$