Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 3 - Derivatives - 3.8 Implicit Differentiation - 3.8 Exercises - Page 200: 34


$\frac{d^2y}{dx^2} = \frac{-3x^2y^4-3x^6}{y^7}$

Work Step by Step

$x^4+y^4=64$ First Derivative: $4x^3+4y^3 \frac{dy}{dx} = 0$ $\frac{dy}{dx} = \frac{-x^3}{y^3}$ Second Derivative: $\frac{d^2y}{dx^2} = \frac{(-3x^2)(y^3)-(-x^3)(3y^2)(\frac{dy}{dx})}{y^6} = \frac{-3x^2y^4-3x^6}{y^7}$
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