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: 45

Answer

$\dfrac{d^2y}{dx^2}=-\dfrac{4}{y^3}.$

Work Step by Step

First Derivative: $\dfrac{d}{dx}(x^2)+\dfrac{d}{dx}(y^2)=\dfrac{d}{dx}(4)\rightarrow$ $2x+\dfrac{dy}{dx}(2y)=0\rightarrow$ $\dfrac{dy}{dx}=-\dfrac{x}{y}$ Second derivative: $\dfrac{d}{dx}(\dfrac{dy}{dx})=\dfrac{d}{dx}(-\dfrac{x}{y})\rightarrow$ $\dfrac{d^2y}{dx^2}=-\dfrac{y-(\dfrac{dy}{dx})(x)}{y^2}=-\dfrac{y^2+x^2}{y^3}=-\dfrac{4}{y^3}.$
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