Calculus 8th Edition

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

Chapter 2 - Derivatives - Review - Exercises - Page 197: 33


$\dfrac {\cos \sqrt {x}}{2\sqrt {x}}-\dfrac {\sin \sqrt {x}}{2}$

Work Step by Step

$\dfrac {d}{dx}\left( \sqrt {x}\cos \left( \sqrt {x}\right) \right) =\left( \dfrac {d}{dx}\left( \sqrt {x}\right) \right) \times \cos \sqrt {x}+\left( \dfrac {d}{dx}\left( \cos \sqrt {x}\right) \right) \times \sqrt {x}=\dfrac {\cos \sqrt {x}}{2\sqrt {x}}-\left( \sin \sqrt {x}\right) \times \sqrt {x}\times \left( \dfrac {d}{dx}\sqrt {x}\right) =\dfrac {\cos \sqrt {x}}{2\sqrt {x}}-\dfrac {\sin \sqrt {x}}{2}$
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