Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Section 3.4 - The Chain Rule - 3.4 Exercises - Page 204: 50



Work Step by Step

$y'=\frac{d{e^{e}}^x}{dx}$ Using the chain rule: $y'=\frac{d{e^{e}}^x}{de^x} \times \frac{d{e^x}}{dx}$ $={e^{e}}^x \times e^x$ $={e^{e^x+x}}$ $y''=\frac{d{e^{e^x+x}}}{dx}$ Using the chain rule: $y''=\frac{d{e^{e^x+x}}}{d e^x+x} \times \frac{de^x+x}{dx}$ $={e^{e^x+x}} \times (e^x+1)$ $=(e^x+1){e^{e^x+x}}$
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