The coth function calculates online the hyperbolic cotangent of a number.

Hyperbolic cotangent 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 cotangent function is written coth, it is defined by the following formula :

`coth(x)=1/(th(x))=(ch(x))/(sh(x))`

Calculation of the hyperbolic cotangent

The hyperbolic cotangent calculator allows through the coth function to calculate online the hyperbolic cotangent of a number.

To calculate the hyperbolic cotangent of a number, enter the number and to apply the coth function. For calculating the hyperbolic cotangent of the following number 2, enter coth(`2`) or directly 2, if the coth button already appears, the result 1.03731472073 is returned.

Derivative of hyperbolic cotangent

The derivative of the hyperbolic cotangent is equal to `-1/(sh(x))^2`.

Antiderivative of hyperbolic cotangent

The antiderivative of the hyperbolic cotangent is equal to `ln(|sh(x|)`.

Limits of hyperbolic cotangent

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

Syntax :

coth(x), where x is a number.

Other notation sometimes used : cotanh

Examples :

coth(`2`), returns 1.03731472073

Derivative hyperbolic cotangent :

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

The derivative of coth(x) is derivative(`"coth"(x)`)=`-1/("sh"(x))^2`

Antiderivative hyperbolic cotangent :

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

An antiderivative of coth(x) is antiderivative(`"coth"(x)`)=`ln("sh"(x))`

Limit hyperbolic cotangent :

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

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

Graphic hyperbolic cotangent :

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

Property of the function hyperbolic cotangent :