Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.4 Exercises: 21

Answer

$y'=-\dfrac{3}{2\sqrt{(3x+5)^3}}.$

Work Step by Step

$y=\dfrac{1}{\sqrt{3x+5}}=(3x+5)^{-\frac{1}{2}}$ Using the Chain Rule: $u=(3x+5)$; $\dfrac{du}{dx}=3$ $\dfrac{dy}{du}=-\dfrac{1}{2\sqrt{u^3}}$ $\dfrac{dy}{dx}=\dfrac{dy}{du}\times\dfrac{du}{dx}=(3)(-\dfrac{1}{2\sqrt{(3x+5)^3}})=-\dfrac{3}{2\sqrt{(3x+5)^3}}.$
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