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: 20

Answer

$f'(x) = \dfrac{5}{2}x^{3/2}-2x^{-1/2}$

Work Step by Step

In order to derivate this function you have to apply the power rule: $\dfrac{d}{dx}(x^n)=nx^{n-1}$ But first let's rewrite the function $f(x) = \dfrac{x^3}{x^{1/2}}-\dfrac{4x}{x^{1/2}}$ $f(x) = x^{5/2}-4x^{1/2}$ then $f'(x) = \dfrac{5}{2}x^{3/2}-2x^{-1/2}$
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