Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - Chapter Review Exercises - Page 164: 65


$$ y'= -(2x+3)^{-3/2} .$$

Work Step by Step

Given $ y=\sqrt{2x+3}$, then we have $$ y'= \frac{2}{2\sqrt{2x+3}} = \frac{1}{\sqrt{2x+3}}=(2x+3)^{-1/2},$$ and the seond derivative $ y''$ is given by $$ y'=-\frac{1}{2} (2x+3)^{-3/2} (2)=-(2x+3)^{-3/2} .$$
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