Calculus 10th Edition

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

Chapter 2 - Differentiation - 2.5 Exercises: 30

Answer

$\dfrac{dy}{dx}=2.$

Work Step by Step

$\dfrac{d}{dx}((4-x)y^2)=\dfrac{d}{dx}(x^3)\rightarrow$ $-y^2+\dfrac{dy}{dx}(2y(4-x))=3x^2\rightarrow$ $\dfrac{dy}{dx}=\dfrac{3x^2+y^2}{8y-2yx}.$ At $(2, 2)\rightarrow\dfrac{dy}{dx}=\dfrac{3(2)^2+2^2}{8(2)-2(2)(2)}=2.$
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