# Hyperbolic Functions

The three most common hyperbolic functions are:

sinh, cosh and tanh

*(pronounced "shine, cosh and than")*

sinh x = \frac{e^{x} − e^{−x}}{2}

cosh x = \frac{e^{x} + e^{−x}}{2}

tanh x = \frac{sinh x}{cosh x} = \frac{e^{x} − e^{−x}}{e^{x} + e^{−x}}

## Derivatives

The derivatives are:

\frac{d}{dx} sinh x = cosh x

\frac{d}{dx} cosh x = sinh x

\frac{d}{dx} tanh x = 1 − tanh^{2} x