Calculus 8th Edition

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

Chapter 6 - Inverse Functions - 6.3* The Natural Exponential Function - 6.3* Exercises: 44

Answer

$2e^{2t}\sec^2(1+e^{2t})$

Work Step by Step

$\frac{d}{dt}\tan(1+e^{2t})$ Use chain rule: $=\sec^2(1+e^{2t})\frac{d}{dt}(1+e^{2t})$ $=\sec^2(1+e^{2t})*e^{2t}*\frac{d}{dt}(2t)$ $=\sec^2(1+e^{2t})*e^{2t}*2$ $=2e^{2t}\sec^2(1+e^{2t})$
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