Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.5 Higher Derivatives - Exercises - Page 135: 13


$$ y''=-\frac{8}{x^3}, \quad y'''=\frac{24}{x^4}.$$

Work Step by Step

Let $ y=\frac{x-4}{x}$; first we simplify $ y $ as follows $$ y= 1-\frac{4}{x}.$$ Now, we get $$ y'=\frac{4}{x^2}$$ $$ y''=-\frac{8}{x^3}, \quad y'''=\frac{24}{x^4}.$$
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