Derivative Formulas

Core Sentence / 核心句

Derivative formulas are reusable shortcuts built from the meaning of derivatives.

中文理解：求导公式不是凭空背的，是导数定义和几何直觉压缩后的工具。

Formula / 公式或规则

Examples: Power Rule, trig derivatives, chain rule.

When To Use / 什么时候用

做 symbolic differentiation、Taylor coefficients、physics rate calculations 时使用。

Watch Out / 易错点

公式快捷，但不要丢掉背后的 local change 意义。

Search and Source Mentions / 搜索与出现位置

Mentioned In / 出现位置

• Chapter 5 · Formula Map
  • exponential derivatives add $(e^x{)}^{\prime }=e^x$ and $(a^x{)}^{\prime }=(\ln a)a^x$ to the formula system
• Chapter 4 · The Structural Map
  • sum, product, and composition organize the rules for complex derivative formulas
• 03 - Derivative Formulas through Geometry · Knowledge Point 1: Derivative Formulas Should Not Feel Like a List of Rules
  • Knowledge Point 1: Derivative Formulas Should Not Feel Like a List of Rules
• 03 - Derivative Formulas through Geometry · 3Blue1Brown - The Essence of Calculus 03 - Derivative Formulas through Geometry
  • 3Blue1Brown - The Essence of Calculus 03 - Derivative Formulas through Geometry
• AP电磁学第1次正课-电荷库仑定律与电场 · Derivatives and Integrals / 微积分工具
  • 这和 03 - Derivative Formulas through Geometry 直接相连：那篇解释了 Power Rule 和 Trigonometric Derivatives 的几何直觉，这里开始把它们作为物理工具使用。
• 03 - Derivative Formulas through Geometry · 1. What This Episode Is About / 这一集在讲什么
  • If I know what a derivative means, how do I actually compute derivative formulas?
• 03 - Derivative Formulas through Geometry · 8. After Watching Summary / 看完压缩版
  • 这一集把 derivative formulas 从“背公式”改造成“看微小变化”：
• 03 - Derivative Formulas through Geometry · 2. Class Flow / 视频脉络
  • 1. 先说明为什么要会算 derivative formulas：现实问题常常用 polynomials, trig functions, exponentials 建模。
• AP电磁学第1次正课-电荷库仑定律与电场 · Reading Guide / 阅读说明
  • - 03 - Derivative Formulas through Geometry

Connected Notes / 连接

• 03 - Derivative Formulas through Geometry
• 04 - Visualizing the Chain Rule and Product Rule
• 05 - What’s So Special About Euler’s Number e
• Exponential Functions
• Natural Logarithm
• Power Rule
• Product Rule
• Chain Rule
• Function Composition
• Trigonometric Derivatives