## Definition of the Derivative Part 1

Definition of the Derivative Part 1
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Be able to explain the definition of the derivative (THE fundamental notion of Calculus) in terms of a limit of the difference quotient and more importantly the Cartesian plot of secant lines vs tangent line to a function.
• What is the formal definition of a derivative?
• What is the limit notation for a derivative?
• How do you approximate a derivative?
• How do you find the average rate of change or slope of the secant line between two points that are very close together on a curve?
• How do you find the slope of a function at a point?
• What happens as h gets smaller and smaller as you try to get two points on a secant line as close together as possible to find the slope at a point of a function?
This lesson shows the formal definition of a derivative using limit notation and explains the concept of the derivative. You will also see how to approximate the derivative of a function at a point. This lesson is a great introduction to derivatives. There is a glitch at the end of this video, so it continues into the next video.
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Reviewed by MathVids Staff on July 25, 2010.