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 - Page 136: 47


$y'=2\pi^2x\cos{(\pi x)}^2.$

Work Step by Step

$u=(\pi x)^2$; $\dfrac{du}{dx}=2\pi^2x$ $\dfrac{d}{du}f(u)=\cos{u}$ $\dfrac{d}{dx}f(x)=\dfrac{d}{du}f(u)\times\dfrac{du}{dx}=2\pi^2x\cos{(\pi x)^2}.$
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