What is a derivative?

What is a derivative? Learn what a derivative is, how to find the derivative using the difference quotient, and how to use the derivative to find the equation of the tangent line. This is a free math video tutorial by Mario’s Math Tutoring.

0:11 What is a Derivative
1:22 Finding the Slope Between 2 Points on a Curve
2:05 Difference Between the Average Rate of Change and the Instantaneous Rate of Change
2:34 Using Limits to Find the Instantaneous Rate of Change
3:15 What is the Difference Quotient
3:23 Notation for the Derivative
3:46 Example 1 Finding the Derivative of f(x)=x^2 Using Difference Quotient
5:02 Using the Derivative to Find the Slope at a Point
5:26 Writing the Equation of the Tangent Line at a Point
6:00 Example 2 f(x)=x^3 - 4x Finding the Derivative to Find the Relative Maximum and Minimums
7:40 Using the Difference Quotient to find the Derivative
7:57 Using the Binomial Expansion Theorem to Simplify
8:54 Setting the Derivative to Zero to Find Turning Points
9:35 Graphing the Polynomial With the Turning Points
10:07 Summary of What the Deriviative is, How to Find it, and How to Use It

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