The function th allows to calculate online the hyperbolic tangent of a number.

Hyperbolic tangent function

The calculator allows you to use most hyperbolic functions, it is possible to calculate the hyperbolic cosine (noted ch or cosh), the hyperbolic sine (noted sh or sinh ), the hyperbolic tangent (noted th or tanh ), and the hyperbolic cotangent (noted coth or cotanh ).

The hyperbolic tangent function is written th, it is defined by the following formula :

`th(x)=(sh(x))/(ch(x))`

Calculation of the hyperbolic tangent

The hyperbolic tangent calculator allows through the th function to calculate online the hyperbolic tangent of a number.

To calculate the hyperbolic tangent of a number, just enter the number and apply the th function. For calculating the hyperbolic tangent of the next number 0, enter th(`0`) or directly 0, if the button th appears already, the result 0 is returned.

Derivative of hyperbolic tangent

The derivative of the hyperbolic tangent is equal to `1/(ch(x))^2`.

Antiderivative of hyperbolic tangent

The antiderivative of the hyperbolic tangent is equal to `ln(ch(x))`.

Limits of hyperbolic tangent

The limits of the hyperbolic tangent exist at `-oo` (minus infinity) and `+oo` (plus infinity):
• The hyperbolic tangent function has a limit in `-oo` which is `-1`.
`lim_(x->-oo)th(x)=-1`
• The hyperbolic tangent function has a limit in `+oo` which is `1`.
`lim_(x->+oo)th(x)=1`

Properties of the hyperbolic tangent function

The hyperbolic tangent function is an odd function, for every real x, `th(-x)=-th(x)`. The consequence for the curve representative of the hyperbolic tangent function is that it admits the origin of the reference point as point of symmetry.

Syntax :

th(x), x is a number.

other notation sometimes used : tanh

Examples :

th(`2`), returns 0.964027580076

Derivative hyperbolic tangent :

To differentiate function hyperbolic tangent online, it is possible to use the derivative calculator which allows the calculation of the derivative of the hyperbolic tangent function

The derivative of th(x) is derivative(`"th"(x)`)=`1/("ch"(x))^2`

Antiderivative hyperbolic tangent :

Antiderivative calculator allows to calculate an antiderivative of hyperbolic tangent function.

An antiderivative of th(x) is antiderivative(`"th"(x)`)=`ln("ch"(x))`

Limit hyperbolic tangent :

The limit calculator allows the calculation of limits of the hyperbolic tangent function.

The limit of th(x) is limit(`"th"(x)`)

Graphic hyperbolic tangent :

The graphing calculator is able to plot hyperbolic tangent function in its definition interval.

Property of the function hyperbolic tangent :