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


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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?


Answer

Outline

Outline for The Derivative

Textbook

Tangent Lines and their Slopes
The Derivative

Today's Homework

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Quiz

Tangent Lines and their Slopes Quiz
The Derivative Quiz

Examples

  • Click to see the exampleLet f(x) = x2 and g(x) = x. Find (f + g)'(4). Does this equal f '(4) + g'(4)?
  • Click to see the exampleDraw the derivative of a given graph.
  • Click to see the exampleLet 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

  • click to see the videoCompute the derivative of f(x) = √(x + 2) using the limit definition of derivative
  • click to see the videoGiven the graph of a smooth curve, draw its derivative
  • click to see the videoGiven the graph of a curve with corners, draw its derivative

Lecture 8 | Index | Lecture 10