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: 44

Answer

$\frac{dy}{dx} = \frac{4x^{0.2}}{5(x^{0.2}+x)^2} $

Work Step by Step

$y = \frac{x}{\sqrt[5] x + x}$ Take Derivative $\frac{dy}{dx} = \frac{(1)(x^{0.2}+x)-(x)(0.2x^{-0.8}+1)}{(x^{0.2}+x)^2} = \frac{x^{0.2}+x-0.2x^{0.2}-x}{(x^{0.2}+x)^2} = \frac{x^{0.2}-0.2x^{0.2}}{(x^{0.2}+x)^2} = \frac{4x^{0.2}}{5(x^{0.2}+x)^2} $
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