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 136: 29


$$\frac{ 720}{x^7}$$

Work Step by Step

Given $$ y= x^{-1}$$ Recall that $(x^n)'=nx^{n-1}$ Then the general derivative is $$ y^{(n)}(x)=(-1)^{n} n ! x^{-n-1}$$ Then $$\frac{d^{6}}{d x^{6}} x^{-1} = 6 ! x^{-7}= \frac{ 720}{x^7}$$
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