Suppose n is a negative integer and f(x) = x n . Use the following steps to
Question:
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
Simplify using the factoring rule (which is valid for n > 0)
b. Use this result to find d/dx (x-7) and d/dx (1/x10).
Transcribed Image Text:
x" = lim х—а х — а a" т х lim х — а f' (a) ха х" — а" — (х — а)(x" -1 + x" ?а + ... a)(x"-1 + x"¯²a + · .. + xa"-2 + a"-1) in
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Related Book For
Calculus Early Transcendentals
ISBN: 978-0321947345
2nd edition
Authors: William L. Briggs, Lyle Cochran, Bernard Gillett
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