内容位置 → 导数依据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。
内容位置 → 导数依据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.
讲解 → 导数依据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。
讲解 → 导数依据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.
内容位置 → 导数的直观理解：Khan Academy 演示依据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。
讲解 → 导数依据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。
内容位置 → 导数的直观理解：Khan Academy 演示依据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.
讲解 → 导数依据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.
math