## Calculus (3rd Edition)

$\sinh x$ and $\tanh \ x$ are increasing hyperbolic functions.
$\sinh x$ and $\tanh \ x$ are increasing hyperbolic functions. We see that $(\sinh x)'=\cosh x$ and $(\tanh x)'=sech^2 \ x$ which means that the first derivative is positive and hence $\sinh x$ and $\tanh \ x$ are increasing.