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: 17

Answer

$\frac{-3}{2\sqrt[4] {x^5}}$

Work Step by Step

Let's rewrite $$y = \frac{6}{\sqrt[4] x}$$ as: $$y = 6x^{-1/4}.$$ We can then use the Power Rule, which says that $\frac{d}{dx}(x^n) = nx^{n-1}$, to find that $$\frac{dy}{dx} = 6\cdot \frac{-1}{4}x^{-1/4 -1} = \frac{-6}{4}x^{-5/4}$$ $$= \frac{-3}{2}x^{-5/4} =\frac{-3}{2\sqrt[4] {x^5}}$$
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