## University Calculus: Early Transcendentals (3rd Edition)

$e^{-3x}$
We apply hyperbolic function formulas: $\cosh x= \dfrac{e^x+e^{-x}}{2}$ and $\sinh x= \dfrac{e^x-e^{-x}}{2}$ Thus, $\cosh (3x) - \sinh (3x)=\dfrac{e^{3x}+e^{-3x}}{2}-\dfrac{e^{3x}-e^{-3x}}{2}=e^{-3x}$