Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - 6.2 Exponential Functions and Their Derivatives - 6.2 Exercises: 41

Answer

$xe^{-3x}(-3x+2)$

Work Step by Step

$y=x^2e^{-3x}$ Use the product rule: $y'=x^2\frac{d}{dx}e^{-3x}+e^{-3x}\frac{d}{dx}x^2$ Use the chain rule to evaluate $\frac{d}{dx}e^{-3x}$: $y'=x^2e^{-3x}\frac{d}{dx}(-3x)+e^{-3x}*2x$ $y'=x^2e^{-3x}*(-3)+2xe^{-3x}$ $y'=-3x^2e^{-3x}+2xe^{-3x}$ Factor out $xe^{-3x}$: $y'=xe^{-3x}(-3x+2)$ $y'=xe^{-3x}(2-3x)$
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