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Derivatives

A derivative is the limit of a difference quotient, measuring local rate of change when that limit exists.

f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}h

Different ways to understand it

Derivative intuition module | Taking derivatives | Differential Calculus | Khan Academy
Khan Academy · en · Explanation
Connection evidence
Candidate from reviewed zh material v1: 在可微的点，导数就是切线的有限斜率。视频将这个想法变成图形任务：让一条直线与曲线在局部的方向相符，再将它的斜率读作导数值。编辑补充：仅仅存在切线还不够；若切线竖直，就没有通常意义下的有限导数。
Derivative intuition module | Taking derivatives | Differential Calculus | Khan Academy
Khan Academy · en · Explanation
Connection evidence
Candidate from reviewed en material v1: At a differentiable point, the derivative is the finite slope of the tangent line. The video turns that idea into a visual task: align a line with the curve locally, then read its slope as the derivative value. Editorial clarification: the existence of a tangent alone is insufficient if its slope is vertical; a finite derivative must exist.

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Explore change, accumulation and approximation through single-variable calculus.