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.
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The chain rule is a method of differentiating a function which is composed of two nested functions. That is, the chain rule provides a general case for taking the x derivative of a function f(g(x)). The chain rule states that the derivative of such a nested function is the product of the derivatives of each function, evaluated at appropriate points. That is, the derivative of such a function is the derivative of f, assuming that g is itself the variable, multiplied by the derivative of g, assuming that x is the variable.
For example, the function sin(x2) can be evaluated using the chain rule. The derivative of sin(y) is cos(y), and the derivative of x2 is 2x. Therefore, the derivative of sin(x2) is 2x cos(x2). The term that is particularly of interest is the argument of the cosine term. The only trick to the chain rule is remembering that the original argument of the outer function must be the argument of its derivative as well.
The chain rule is one of the basic rules of differentiation. It would be possible to step through the limit definition of a derivative every time a composite or nested function came up, but the chain rule provides a much more efficient method and is widely used wherever calculus is applied.