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: 15

Answer

$y'=-\dfrac{x}{\sqrt[4]{(9-x^2)^3}}$

Work Step by Step

$u=(9-x^2)$; $\dfrac{du}{dx}=-2x$ $y(u)=2u^{\frac{1}{4}};\dfrac{dy}{du}=\dfrac{1}{2\sqrt[4]{u^3}}$ $\dfrac{dy}{dx}=\dfrac{dy}{du}\times\dfrac{du}{dx}=(-2x)(\dfrac{1}{2\sqrt[4]{(9-x^2)^3}})=-\dfrac{x}{\sqrt[4]{(9-x^2)^3}}$
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