Suppose n is a negative integer and f(x) = x n . Use the following steps to

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Suppose n is a negative integer and f(x) = xn. Use the following steps to prove that f'(a) = nan - 1, which means the Power Rule for positive integers extends to all integers.

a. Assume that m = - n, so that m > 0. Use the definition

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Simplify using the factoring rule (which is valid for n > 0)

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b. Use this result to find d/dx (x-7) and d/dx (1/x10). 

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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