Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - 2.3 Differentiation Formulas - 2.3 Exercises: 44

Answer

$f'(x)=\dfrac{ad-cb}{c^2x^2+2cdx+d^2}$

Work Step by Step

Identify the functions in order to apply quotient rule $h=ax+b$ $h'=a$ $g=cx+d$ $g'=c$ Apply quotient rule $(\dfrac{h}{g})'=\dfrac{h'g-hg'}{g^2}$ $f'(x)=\dfrac{a(cx+d)-c(ax+b)}{(cx+d)^2}$ $f'(x)=\dfrac{acx+ad-acx-cb}{c^2x^2+2cdx+d^2}$ $f'(x)=\dfrac{ad-cb}{c^2x^2+2cdx+d^2}$
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