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: 22

Answer

$\frac{d^2y}{dx^2}=2cosx-2xsinx-x^2cosx-(2x+4)sinx$

Work Step by Step

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