2.7 The Derivative

By the end of your studying, you should know:
Onscreen applet instructions: Use the slider to control the value of h. Note that the number of difference quotients computed and plotted increases as h>0. The button under the slider shows and hides the derivative curve. Whenever you like, you can compare a computed set of difference quotients with the derivative. What is the geometrical significance of the limit of the difference quotient as h > 0?
ExamplesLet f(x) = x^{2} and g(x) = x. Find (f + g)' (4). Does this equal f '(4) + g'(4)?
Draw the derivative of the following 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)?
VideosSee short videos of worked problems for this section.
QuizExercisesSee Exercises for 2.7 The Derivative (PDF).Work online to solve the exercises for this section, or for any other section of the textbook. 
Resources on the WebInformation on NewtonBiographical data from St. Andrew's University's Web site Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics"
Information on Leibniz
Calculus Applications
Derivatives

Interesting Application
Average reaction rates and instantaneous reaction rates in chemistry can be quite different. 
2.6 Tangent Lines and Their Slopes  Table of Contents  2.8 Differentiation Rules 
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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel