The following sections of this BookRags Literature Study Guide is offprint from Gale's For Students Series: Presenting Analysis, Context, and Criticism on Commonly Studied Works: Introduction, Author Biography, Plot Summary, Characters, Themes, Style, Historical Context, Critical Overview, Criticism and Critical Essays, Media Adaptations, Topics for Further Study, Compare & Contrast, What Do I Read Next?, For Further Study, and Sources.
(c)1998-2002; (c)2002 by Gale. Gale is an imprint of The Gale Group, Inc., a division of Thomson Learning, Inc. Gale and Design and Thomson Learning are trademarks used herein under license.
The following sections, if they exist, are offprint from Beacham's Encyclopedia of Popular Fiction: "Social Concerns", "Thematic Overview", "Techniques", "Literary Precedents", "Key Questions", "Related Titles", "Adaptations", "Related Web Sites". (c)1994-2005, by Walton Beacham.
The following sections, if they exist, are offprint from Beacham's Guide to Literature for Young Adults: "About the Author", "Overview", "Setting", "Literary Qualities", "Social Sensitivity", "Topics for Discussion", "Ideas for Reports and Papers". (c)1994-2005, by Walton Beacham.
All other sections in this Literature Study Guide are owned and copyrighted by BookRags, Inc.
Differentiation of algebraic functions works by one of the simplest rules in calculus. Each component of the algebraic function is differentiated separately, and then the differentials are added together. If the components of the algebraic function are the variable taken to different powers and multiplied by coefficients, the process is even easier.
First, the power of the variable is decreased by one, so that if the original power is x3, the result contains a power of x2. Then, the original power of the variable is multiplied by the coefficient of the term for the new coefficient. In this manner, 5x4 becomes 20x3 when differentiated once. Constant terms, of course, disappear.
Each of these rules has a specific name, within calculus. The rule that a constant's derivative is zero is, of course, the constant derivative rule. The power rule for positive integer powers of x states that, when taking a derivative of a function of a positive integer power of x, the power of the variable is decreased by one and the function is multiplied by the original power. The constant multiple rule simply affirms that the derivative of a constant times a function is the same as the constant times the derivative of the function. Finally, the sum and difference rule states that the derivatives of sums and differences of algebraic terms are the same as the sums and differences of the derivatives.
The differentiation of algebraic functions is probably one of the most used skills in calculus. Many rate of change problems occur at linear rates, and still more can be expressed in terms of algebraic functions. Since calculus is largely the study of rates of change, this skill and information become particularly useful.