tiwe0/geochat/derivative-tangent

Claude Code and agent skill by tiwe0/geochat

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导数几何意义、切线、法线、切点和参数切线条件技能。

Install

npx vskill@latest install tiwe0/geochat/derivative-tangent

SKILL.md

导数与切线

适用于求切线方程、过定点切线、公切线、切点参数和切线与函数关系。必须区分切点横坐标和给定点坐标。

工作顺序：

  1. 设切点并写出 f'(x0) 作为切线斜率。
  2. 用点斜式建立切线方程。
  3. 过定点切线题把定点代入切线方程求切点。
  4. 可视化时同时画函数、切点、切线和给定点。

关键规则：Tangent(P,f) 使用 x(P) 作为切点横坐标，给定点不必在函数上；切点应另建为 (x0,f(x0))。切线斜率是 f'(x0)；法线斜率仅在切线斜率非零时为 -1/f'(x0)，水平切线对应竖直法线。

原生输入小例子

在空白构图中逐行输入；名称冲突时改名，不覆盖用户对象。

ggb
fTan(x) = x^2
x0Tan = 1
TouchTan = (x0Tan, fTan(x0Tan))
tangentTan = Tangent(TouchTan, fTan)
slopeTan = Slope(tangentTan)
OffCurveTan = (1, 5)
tangentFromXOnlyTan = Tangent(OffCurveTan, fTan)
flatFnTan(x) = 4
flatTangentTan = Tangent(0, flatFnTan)

预期：TouchTan=(1,1)，tangentTan 与 tangentFromXOnlyTan 都是 y=2x-1，slopeTan=2；这证明函数版 Tangent 读取的是点的横坐标，不是要求点落在函数上。正常验证将切点代入直线并核对斜率；边界验证 flatTangentTan 为 y=4，其法线应为竖线 x=0；退化验证在不可导点不要强行生成唯一切线。

官方参考：Tangent、Slope、Derivative。

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