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4:49
2026-08-03

The Derivative: From Secant Slopes to Instantaneous Change

US Freshman Calc I
US Freshman Calc I@chinamusk
This English Calculus I lecture derives the derivative from secant slopes, works f'(3) for f(x)=x^2 from the limit definition, and connects the result to tangent lines, instantaneous velocity, and differentiability.
Sources used:
  • OpenStax-derived Section 3.1: Defining the Derivative
  • OpenStax Calculus Volume 1: The Derivative as a Function
US Freshman Calc I
US Freshman Calc I@chinamusk

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