Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 2 - The Derivative - 2.5 Derivatives of Trigonometric Functions - Exercises Set 2.5 - Page 151: 21


$\frac{d^2y}{dx^2}=5\cos x-x\sin x$

Work Step by Step

$y=xsinx-3cosx$ $\frac{dy}{dx}=(sinx+x\times{cosx})-3(-sinx)$ $\frac{dy}{dx}=(sinx+xcosx)+3sinx$ $\frac{dy}{dx}=4sinx+xcosx$ $\frac{d^2y}{dx^2}=4(cosx)+(cosx+x\times{(-sinx)})$ $\frac{d^2y}{dx^2}=4cosx+(cosx-xsinx)$ $\frac{d^2y}{dx^2}=5\cos x-x\sin x$
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