For questions related to hyperbolic functions: $\sinh$, $\cosh$, $\tanh$, and so on.
The hyperbolic functions are analogs of the usual trigonometric functions; we may define such functions as the hyperbolic sine
$$\sinh{x} = \frac{e^x - e^{-x}}{2}$$
and the hyperbolic cosine
$$\cosh{x} = \frac{e^x + e^{-x}}{2}$$
as well as the hyperbolic tangent
$$\tanh{x} = \frac{\sinh{x}}{\cosh{x}}=\frac{e^x - e^{-x}}{e^x + e^{-x}}$$
These functions are differentiable. More precisely, $\cosh'=\sinh$, $\sinh'=\cosh$, and $\tanh'=1-\tanh^2$.
Just as the point $(\cos{t}, \sin{t})$ describes a point on the unit circle $x^2 + y^2 = 1$, the point $(\cosh{t}, \sinh{t})$ defines a point on the unit hyperbola $x^2 - y^2 = 1$.
Reference: Hyperbolic function.
