Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.3 Product and Quotient Rules - Exercises - Page 121: 3



Work Step by Step

Applying product rule, $\frac{d}{dx}[√x(1-x^{3})]$= $[\frac{d(√x)}{dx} $•$(1-x^{3})]$ + [√x •$\frac{d}{dx}(1-x^{3})$] = $\frac{1}{2}x^{\frac{1}{2}-1}(1-x^3) + (\frac{d(1)}{dx}-\frac{d(x^{3})}{dx})√x$ = $\frac{1-x^{3}}{2√x} + (0-3x^{2})√x$ =$\frac{1-x^{3}}{2√x} - 3x^{5/2}$ Simplifying, we get f'(x)= $\frac{1-7x^{3}}{2√x}$
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