Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.3 Exercises: 50

Answer

$y'=x\cos(x)$

Work Step by Step

$y=f(x)+g(x)\rightarrow f(x)=x\sin(x)$; $g(x)=\cos(x)$ Product Rule $f'(x)=((u(x)(v(x))’=u’(x)v(x)+u(x)v’(x))$ $u(x)=x ;u’(x)=1 $ $v(x)=\sin(x) ; v’(x)=\cos(x) $ $f'(x)=\sin(x)+x\cos(x)$ $g'(x)=\dfrac{d}{dx}(\cos(x))=-\sin(x)$ $y'=f'(x)+g'(x)=x\cos(x)$
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