Calculus, 10th Edition (Anton)

Published by Wiley

Chapter 2 - The Derivative - 2.5 Derivatives of Trigonometric Functions - Exercises Set 2.5 - Page 151: 19

Answer

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

Work Step by Step

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

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