Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Review - Exercises: 3

Answer

$\frac{3}{2}\sqrt x-\frac{1}{2\sqrt x}-\frac{1}{\sqrt {x^{3}}}$

Work Step by Step

Start with the function $y=\frac{x^{2}-x+2}{x^{1/2}}$. Divide each term of the fraction: $y=x^{3/2}-x^{1/2}+2x^{-1/2}$. Differentiate using the power rule for each term: $y'=\frac{3}{2}x^{1/2}-\frac{1}{2}x^{-1/2}-x^{-3/2}$. Change from fractional power form to radical form to arrive at the answer: $\frac{3}{2}\sqrt x-\frac{1}{2\sqrt x}-\frac{1}{\sqrt {x^{3}}}$.
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