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: 52

Answer

$f'(x)=\cos(2x)$.

Work Step by Step

Product Rule $f'(x)=((u(x)(v(x))’=u’(x)v(x)+u(x)v’(x))$. $u(x)=\sin(x) ;u’(x)=\cos(x) $ $v(x)=\cos(x) ;v’(x)=-\sin(x) $ $f'(x)=(\cos(x))(\cos(x))+(-\sin(x))(\sin(x))$ $=\cos^2(x)-\sin^2(x)=\cos(2x).$
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