Answer
$f^{(n)}(x)=\dfrac{(-1)^n(n!)}{x^{n+1}}$
Work Step by Step
$f'(x)=\dfrac{(-1)^1(1)}{x^2}.$
$f''(x)=\dfrac{(-1)^2(1)(2)}{x^3}.$
$f'''(x)=\dfrac{(-1)^3(1)(2)(3)}{x^4}.$
...
$f^{(n)}(x)=\dfrac{(-1)^n(n!)}{x^{n+1}}.$
Calculus 10th Edition
by Larson, Ron; Edwards, Bruce H.
Published by
Brooks Cole
ISBN 10:
1-28505-709-0
ISBN 13:
978-1-28505-709-5
Chapter 2 - Differentiation - 2.3 Exercises - Page 128: 120
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