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: 17

Answer

$y'=\dfrac{3}{2}x^{1/2}+2x^{-1/2}-\dfrac{3}{2}x^{-3/2}$

Work Step by Step

Reduce the expression $y=\dfrac{x^2+4x+3}{\sqrt{x}}=\dfrac{x^2+4x+3}{x^{1/2}}$ $y=\dfrac{x^2}{x^{1/2}}+\dfrac{4x}{x^{1/2}}+\dfrac{3}{x^{1/2}}$ $y=x^{3/2}+4x^{1/2}+3x^{-1/2}$ Then apply power rule to derivate $y'=(\dfrac{3}{2})x^{3/2-1}+4(\dfrac{1}{2})x^{1/2-1}-3(\dfrac{1}{2})x^{-1/2-1}$ $y'=\dfrac{3}{2}x^{1/2}+2x^{-1/2}-\dfrac{3}{2}x^{-3/2}$
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