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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?
Answer
Outline
Outline for
Differentiation Rules
Textbook
Differentiation Rules
Today's Homework
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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 x^{n} is nx^{n–1}
 Find derivative of t^{17} at t = 1
 find f'(8) if f(x) = cuberoot of x
 Statement of the product rule
 Find derivative of (3x + 2)x^{1/2}
 Find derivative of sin(x)(x^{3} + 1)
 Statement of the quotient rule
 Find derivative of (x + 3)/(x^{2} + 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 (x^{3} + 1)^{1/2}
