Answer
$f’(x) =- \frac{2}{(x-2)^{2}}$
Work Step by Step
$f(x) = \frac{x}{x-2} $
$Quotient$ $Rule:$
$f’(x) = \frac{(x-2)\frac{d}{dx}(x)-(x)\frac{d}{dx}(x-2)}{(x-2)^{2}}$
$f’(x) = \frac{(x-2)-(x)}{(x-2)^{2}}$
$f’(x) =- \frac{2}{(x-2)^{2}}$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 3 - Differentiation - 3.3 Product and Quotient Rules - Exercises - Page 121: 7
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