hyperbolic tangent

Calculus th

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Function : th

Summary :

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

Th online

Description :

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))`

  1. Calculation of the hyperbolic tangent
  2. 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.

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

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

  7. 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`

  8. Properties of the hyperbolic tangent function
  9. 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.


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


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 :

The hyperbolic tangent function is an odd function.
Calculate online with th (hyperbolic tangent)
See also :
  • Exponential : exp. The function exp calculates online the exponential of a number.
  • Hyperbolic cosine : ch. The function ch calculates online the hyperbolic cosine of a number
  • Hyperbolic cotangent : coth. The coth function calculates online the hyperbolic cotangent of a number.
  • Hyperbolic sine : sh. The sh function allows to calculate online the hyperbolic sine of a number.
  • Hyperbolic tangent : th. The function th allows to calculate online the hyperbolic tangent of a number.
  • Arccosine : arccos. The arccos function allows the calculation of the arc cosine of a number. The arccosine function is the inverse functions of the cosine function.
  • Arcsine : arcsin. The arcsin function allows the calculation of the arc sine of a number. The arcsine function is the inverse function of the sine function.
  • Arctangent : arctan. The arctan function allows the calculation of the arctangent of a number. The arctangent function is the inverse functions of the tangent function.
  • Cosine : cos. The cos trigonometric function calculates the cosine of an angle in radians, degrees or gradians.
  • Cotangent : cotan. The cotan trigonometric function to calculate the cotangent of an angle in radians, degrees or gradians.
  • Trigonometric expansion : expand_trigo. The calculator makes it possible to obtain the trigonometric expansion of an expression.
  • Trigonometric linearization : linearization_trigo. Calculator that allows to linearize a trigonometric expression.
  • Simplify Calculator : simplify. Calculator wich can simplify an algebraic expression online.
  • Sine : sin. The sin trigonometric function to calculate the sine of an angle in radians, degrees or gradians.
  • Tangent : tan. The tan trigonometric function to calculate the tangent of an angle in radians, degrees or gradians.
  • Trigonometric Calculator : trig_calculator. Calculator wich uses trigonometric formula to simplify trigonometric expression.