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: 62

Answer

$f'(\frac{\pi}{4})=1$

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) $ $v(x)=\sin(x)+\cos(x) ;v’(x)=\cos(x)-\sin(x)$ $f'(x)=(\cos(x))(\sin(x)+\cos(x))+(\sin(x))(\cos(x)-\sin(x))$ $=(2\cos(x)\sin(x))+(\cos^2(x)-\sin^2(x))$ $=\sin(2x)+\cos(2x)$ $f'(\frac{\pi}{4})=sin(\frac{\pi}{2})+\cos(\frac{\pi}{2})=1$.
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