Calculus on Demand at Dartmouth College Lecture 8 | Index | Lecture 10 Lecture 9

## Resources

Math 3 Course Syllabus
Practice Exams

# Contents

In this lecture we continue the discussion of tangent lines, and define the derivative of a function at a point. (There should be drum rolls and much clapping in the background here. The definition of the derivative has been our goal from the first lecture.)

### Quick Question

Does this function have a unique tangent line at x = 0?

### Outline

Outline for The Derivative

### Textbook

Tangent Lines and their Slopes
The Derivative

### Quiz

Tangent Lines and their Slopes Quiz
The Derivative Quiz

### Examples

• Let f(x) = x2 and g(x) = x. Find (f + g)'(4). Does this equal f '(4) + g'(4)?
• Draw the derivative of a given graph.
• Let g(x) = 1/x. Find g'(x), g''(x), and g'''(x), and graph them. Can you find a formula for the nth derivative of g(x)?

### Videos

• Compute the derivative of f(x) = √(x + 2) using the limit definition of derivative
• Given the graph of a smooth curve, draw its derivative
• Given the graph of a curve with corners, draw its derivative

Lecture 8 | Index | Lecture 10