Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - 2.3 Differentiation Formulas - 2.3 Exercises: 35

Answer

$y'=-\dfrac{1}{s^2}+\dfrac{3}{2\sqrt{x^5}}$

Work Step by Step

Reduce the expression $y=\dfrac{s-\sqrt{s}}{s^2}=\dfrac{s}{s^2}+\dfrac{\sqrt{s}}{s^2}$ $y=s^{-1}-s^{-3/2}$ Apply power rule $y'=(-1)s^{-1-1}-(-\dfrac{3}{2})s^{-3/2-1}$ $y'=-s^{-2}+(\dfrac{3}{2})s^{-5/2}$ $y'=-\dfrac{1}{s^2}+\dfrac{3}{2\sqrt{x^5}}$
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