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: 50

Answer

$\dfrac{d^2y}{dx^2}=-\dfrac{32}{9y^5}.$

Work Step by Step

$\dfrac{d}{dx}(y^3)=\dfrac{d}{dx}(4x)\rightarrow$ $\dfrac{dy}{dx}=\dfrac{4}{3y^2}$ Second Derivative: $\dfrac{d}{dx}(\dfrac{dy}{dx})=\dfrac{d}{dx}(\frac{4}{3}y^{-2})\rightarrow$ $\dfrac{d^2y}{dx^2}=\dfrac{dy}{dx}(-\dfrac{8}{3y^3})=-\dfrac{32}{9y^5}.$
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