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


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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

  • Click to see the exampleDifferentiate h(x) = (x + 2)4
  • Click to see the exampleRobert 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?
  • Click to see the exampleFind 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

  • click to see the videoDerivative of xn is nxn–1
  • click to see the videoFind derivative of t17 at t = 1
  • click to see the videofind f'(8) if f(x) = cuberoot of x
  • click to see the videoStatement of the product rule
  • click to see the videoFind derivative of (3x + 2)x1/2
  • click to see the videoFind derivative of sin(x)(x3 + 1)
  • click to see the videoStatement of the quotient rule
  • click to see the videoFind derivative of (x + 3)/(x2 + 7)
  • click to see the videoFind derivative of tan(x)
  • click to see the videoStatement 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
  • click to see the videoDescribing the velocity of a duck flying along a parameterized curve. This video is 17+ minutes
  • click to see the videoStatement of the chain rule, examples of compositions of functions
  • click to see the videoFind derivative of (x3 + 1)1/2

Lecture 9 | Index | Lecture 11