The Definition Of A Derivative

This animation builds the formal definition of a derivative from a secant line through two points on a curve. As the second point slides toward the first, the secant line rotates into the tangent line, and the slope formula becomes the limit definition f'(x) = lim(h→0) [f(x+h) - f(x)] / h. It helps students see why the derivative is defined as a limit rather than just memorized as a formula, useful for anyone starting differential calculus.

16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy

The prompt that made it

Definition

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• Show how the definition of a derivative applies to a specific function like x squared
• Animate the definition of a limit using epsilon-delta reasoning
• Compare the derivative definition to the definition of an integral as a limit of sums

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