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: 47

Answer

$\dfrac{d^2y}{dx^2}=-\dfrac{36}{y^3}.$

Work Step by Step

$\dfrac{d}{dx}(x^2)-\dfrac{d}{dx}(y^2)=\dfrac{d}{dx}(36)\rightarrow$ $2x-\dfrac{dy}{dx}(2y)=0\rightarrow\dfrac{dy}{dx}=\dfrac{x}{y}.$ Second Derivative: $\dfrac{d}{dx}(\dfrac{dy}{dx})=\dfrac{d}{dx}(\dfrac{x}{y})\rightarrow$ $\dfrac{d^2y}{dx^2}=\dfrac{y-\dfrac{dy}{dx}(x)}{y^2}=\dfrac{y^2-x^2}{y^3}=-\dfrac{36}{y^3}.$
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