2.8 Differentiation Rules



If there had not been easily applied rules for finding the derivative of most functions used in modeling, the derivative would not be as powerful a tool as it has turned out to be. Using the limit definition, general rules are developed for constant multiples of a function; sums, products, reciprocals, quotients, and compositions of functions. Along with the Power Rule, these rules permit the calculation of the derivative of a remarkably large number of functions.

By the end of your studying, you should know:

On-screen 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.


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.


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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