Hyperbolic tangent. To be associated with the other hyperbolic functions, like sinh and cosh. Like tan, it is equivalent to sinh/cosh (tan = sin/cos). Pronounced "tanch," like "ranch." When finding a value for tanh(x), it may be useful to use the following:
e2x-1
-------
e2x+1
Indefinite integral of tanh(x): x - ln(e2x+1)/2
Derivative of tanh(x): sech2(x)