Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.4 Exercises: 49

Answer

$h'(x)=2\cos{4x}.$

Work Step by Step

You can use the product rule to differentiate but it would be much easier to use the identity $(2\sin{x}\cos{x}=\sin{2x})$ to rewrite $h(x)$ as $\dfrac{\sin{4x}}{2}$ $u=4x$; $\dfrac{du}{dx}=4$ $\dfrac{d}{du}h(u)=\dfrac{\cos{u}}{2}$ $\dfrac{d}{dx}h(x)=\dfrac{d}{du}h(u)\times\dfrac{du}{dx}=2\cos{4x}.$
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