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: 17

Answer

$f'(x)=cos(x)-xsin(x); f'(\frac{\pi}{4})=\frac{4\sqrt 2-\pi\sqrt 2}{8}$.

Work Step by Step

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) $ $f'(x)=(1)(cos(x))+(x)(-sin(x))=\cos(x)-x\sin(x)$ $f'(\frac{\pi}{4})=cos(\frac{\pi}{4})-(\frac{\pi}{4})(sin(\frac{\pi}{4}))=\frac{4\sqrt 2-\pi\sqrt 2}{8}$.
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