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 - Page 140: 18


$y=-\dfrac{3}{2\sqrt[5]{ x^2}}-\dfrac{1}{x^2}$

Work Step by Step

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