2.8 Differentiation Rules

By the end of your studying, you should know:
Onscreen applet instructions: The table displayed shows the values of the difference quotients of fg for the given value of h and at various points x. The value of h may be controlled by the slider so that one can investigate the limit of the difference quotients as h → 0. The hide/show button at the bottom will show an additional column of values for comparison with the derivative fg′ + f′g.
ExamplesDifferentiate 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.
VideosSee short videos of worked problems for this section.
QuizExercisesSee Exercises for 2.8 Differentiation Rules (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
Table of Differentiation Rules

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2.7 The Derivative  Table of Contents  2.9 Derivatives of the Trigonometric Functions 
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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel