Hyperbolic function/R/Hyperbolic tangent/Definition

Hyperbolic tangent

The function

$\mathbb {R} \longrightarrow \mathbb {R} ,x\longmapsto \tanh x={\frac {\sinh x}{\cosh x}}={\frac {e^{x}-e^{-x}}{e^{x}+e^{-x}}},$

is called hyperbolic tangent.