#### 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
$$\frac{d^{6}}{d x^{6}} x^{-1} = 6 ! x^{-7}= \frac{ 720}{x^7}$$

Published by
W. H. Freeman

ISBN 10:
1464125260

ISBN 13:
978-1-46412-526-3

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

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