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: 38

Answer

$y'=2-x(2\tan{x}+x\sec^2{x}).$

Work Step by Step

$y=f(x)+g(x)\rightarrow f(x)=-x^2\tan{x}$ ; $g(x)=2x$ Product Rule $(f’(x)=(u(x)(v(x))’=u’(x)v(x)+u(x)v’(x))$ $u(x)=-x^2 ;u’(x)=-2x $ $v(x)=\tan{x} ;v’(x)=\sec^2{x} $ $f'(x)=(-2x)(\tan{x})+(\sec^2{x})(-x^2)$ $=-x(2\tan{x}+x\sec^2{x}).$ $g'(x)=2$ $y'=f'(x)+g'(x)=2-x(2\tan{x}+x\sec^2{x}).$
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