Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 3: Derivatives - Practice Exercises - Page 178: 44



Work Step by Step

Take the derivative of the equation on each side separately. Apply chain rule when differentiating the "y" variables since we are differentiating with respect to x: $\frac{4}{5}\times5x^{-1/5}+\frac{6}{5}\times10y^{1/5}\frac{dy}{dx}=0$ Move all terms with dy/dx to one side of the equation, and isolate dy/dx: $12y^{1/5}\frac{dy}{dx}=-4x^{-1/5}$ $\frac{dy}{dx}=\frac{-4x^{-1/5}}{12y^{1/5}}$ $\frac{dy}{dx}=\frac{-4}{12x^{1/5}y^{1/5}}$
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