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: 53

Answer

$y'=4x\cos(x)+(2-x^2)\sin(x)$.

Work Step by Step

$y=f(x)+g(x)\rightarrow f(x)=2x\sin(x)$; $g(x)=x^2cos(x)$ Using Product Rule: $f'(x)=((u(x)(v(x))’=u’(x)v(x)+u(x)v’(x))$ $u(x)=2x ;u’(x)=2 $ $v(x)=\sin(x) ;v’(x)=\cos(x) $ $f'(x)=2x\cos(x)+2\sin(x)$. Using Product Rule: $g'(x)=((u(x)(v(x))’=u’(x)v(x)+u(x)v’(x))$ $u(x)=x^2 ;u’(x)=2x $ $v(x)=\cos(x) ;v’(x)=-\sin(x) $ $g'(x)=(2x)(\cos(x))-x^2\sin(x)$. Using Sum Rule: $y'=f'(x)+g'(x)=4x\cos(x)+(2-x^2)\sin(x)$.
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