Introduction to the Derivative & Rates of Change | Calculus I (9)

Welcome to the ninth lecture in our Calculus I series, where we officially begin our journey into differential calculus with the introduction of the derivative!

In this video, we build upon our understanding of limits to define one of the most important concepts in all of calculus. We will start by revisiting the slope of a secant line and see how it leads us to the idea of a tangent line, which represents the instantaneous rate of change of a function at a single point. This leads us directly to the formal, limit-based definition of the derivative. We will then work through a detailed example, applying both definitions of the derivative to find the slope of a tangent line.

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► Watch the previous video in this series:    • Review of Functions (Domain, Range & Symme...  
► Watch the next video in this series:    • Review of Functions (Domain, Range & Symme...  

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TIMESTAMPS:
00:20 - From Slope of a Secant Line...
02:05 - ...to the Slope of a Tangent Line
03:13 - What is a Derivative? (Instantaneous Rate of Change)
03:56 - The Formal Definition of the Derivative
08:10 - Example: Finding the Derivative Using Both Definitions