Answer
$e^{-3x}$
Work Step by Step
We apply hyperbolic function formulas:
$ \cosh x= \dfrac{e^x+e^{-x}}{2}$ and $ \sinh x= \dfrac{e^x-e^{-x}}{2}$
Thus, $\cosh (3x) - \sinh (3x)=\dfrac{e^{3x}+e^{-3x}}{2}-\dfrac{e^{3x}-e^{-3x}}{2}=e^{-3x}$
University Calculus: Early Transcendentals (3rd Edition)
by Hass, Joel R.; Weir, Maurice D.; Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0321999584
ISBN 13:
978-0-32199-958-0
Chapter 7 - Section 7.3 - Hyperbolic Functions - Exercises - Page 417: 8
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