Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.3 Exercises: 120

Answer

$f^{(n)}(x)=\dfrac{(-1)^n(n!)}{x^{n+1}}$

Work Step by Step

$f'(x)=\dfrac{(-1)^1(1)}{x^2}.$ $f''(x)=\dfrac{(-1)^2(1)(2)}{x^3}.$ $f'''(x)=\dfrac{(-1)^3(1)(2)(3)}{x^4}.$ ... $f^{(n)}(x)=\dfrac{(-1)^n(n!)}{x^{n+1}}.$
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