Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 4 - Calculating the Derivative - 4.1 Techniques for Finding Derivatives - 4.1 Exercises - Page 207: 18

Answer

$$\dfrac{dy}{dx}= \frac{2}{3} x^{-4 / 3}$$

Work Step by Step

Since $ y=\dfrac{-2}{\sqrt[3]{x}} = -2 x^{-1 / 3}$ Using the rule $\frac{d}{dx}x^n=nx^{n-1},$ then \begin{align*} \dfrac{dy}{dx}&= (-2)\frac{-1}{3}x^{-4/3}\\ &=\frac{2}{3} x^{-4 / 3}\end{align*}
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