Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 3 - Derivatives - 3.4 The Product and Quotient Rules - 3.4 Exercises - Page 160: 52


$$f'(x)=\frac{-1}{x^2}$$ $$f''(x)=\frac{3}{x^3}$$ $$f'''(x)=\frac{-12}{x^4}$$

Work Step by Step

The original function $f(x)=\frac{1}x$ can be rewritten as $f(x)=x^{-1}$ due to the definition of the derivatives, $f'(x)=-x^{-2}$ the definition of the derivatives can be applied again: $f''(x)=3x^{-3}$ and for the third derivative, it is applied one last time: $f'''(x)=-12x^{-4}$
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