Calculus on Demand at Dartmouth College Lecture 9 | Index | Lecture 11 Lecture 10

## Resources

Math 3 Course Syllabus
Practice Exams

# Contents

In this lecture we compute (using limits) the derivatives of polynomial functions and functions related to them. We will find that these computations lead to simple rules and formulas that we can remember easily.

### Quick Question

What is the value of the slope of the line whose graph is that of the sum of the two linear functions 2x and 3x?

### Outline

Outline for Differentiation Rules

### Textbook

Differentiation Rules

### Quiz

Differentiation Rules Quiz

### Examples

• Differentiate h(x) = (x + 2)4
• Robert throws a rock into a lake, which creates a circle of ripples which moves away from the point of impact at a constant speed of 50 centimeters per second. What is the rate of change in the area of the circle after 1 second? After 10 seconds? After t seconds?
• Find the instantaneous rate of change of the volume of a cube with respect to the length of its edge, x, when x equals 4 inches.

### Videos

• Derivative of xn is nxn–1
• Find derivative of t17 at t = 1
• find f'(8) if f(x) = cuberoot of x
• Statement of the product rule
• Find derivative of (3x + 2)x1/2
• Find derivative of sin(x)(x3 + 1)
• Statement of the quotient rule
• Find derivative of (x + 3)/(x2 + 7)
• Find derivative of tan(x)
• Statement of the chain rule, viewing the rule as describing related rates of change, example: rate of change of volume of balloon when radius changes. This video is 18+ minutes
• Describing the velocity of a duck flying along a parameterized curve. This video is 17+ minutes
• Statement of the chain rule, examples of compositions of functions
• Find derivative of (x3 + 1)1/2

Lecture 9 | Index | Lecture 11