Calculus 10th Edition

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

Chapter 2 - Differentiation - Review Exercises: 39

Answer

$y'=-x\sin{x}.$

Work Step by Step

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