Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Section 3.2 - The Product and Quotient Rules - 3.2 Exercises: 26

Answer

$f'(x)=\dfrac{ad-bc}{(cx+d)^{2}}$

Work Step by Step

$f(x)=\dfrac{ax+b}{cx+d}$ (Here, $a$, $b$, $c$ and $d$ are constants) Differentiate using the quotient rule: $f'(x)=\dfrac{(cx+d)(ax+b)'-(ax+b)(cx+d)'}{(cx+d)^{2}}=...$ $...=\dfrac{(cx+d)(a)-(ax+b)(c)}{(cx+d)^{2}}$ Simplify: $...=\dfrac{acx+ad-acx-bc}{(cx+d)^{2}}=\dfrac{ad-bc}{(cx+d)^{2}}$
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