## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 3 - Differentiation - 3.5 Higher Derivatives - Exercises - Page 136: 29

#### Answer

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

#### 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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