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 122: 26



Work Step by Step

Using the quotient rule, we have $f'(x)=\frac{\sqrt {x}\frac{d}{dx}(3x^{3}-x^{2}+2)-(3x^{3}-x^{2}+2)\frac{d}{dx}(\sqrt {x})}{(\sqrt {x})^{2}}$ $=\frac{\sqrt {x}(9x^{2}-2x)-(3x^{3}-x^{2}+2)\frac{1}{2\sqrt {x}}}{x}$ $=\frac{9x^{5/2}-2x^{3/2}-\frac{3x^{5/2}}{2}+\frac{x^{3/2}}{2}-x^{-1/2}}{x}$ $=\frac{15x^{5/2}}{2x}-\frac{3x^{3/2}}{2x}-\frac{x^{-1/2}}{x}$ $=\frac{15}{2}x^{3/2}-\frac{3}{2}x^{1/2}-x^{-3/2}$
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