exponential

Quizzes and games : function, complex numbers

The function exp calculates online the exponential of a number.

Quizzes and games : function, complex numbers

Exp, online calculus

Summary :

The function exp calculates online the exponential of a number.

exp online

Description :

Exponential function

The exponential function is defined for any number belonging to the interval ]`-oo`,`+oo`[, it note exp.

  1. Calculation of the exponential
  2. With the exponential calculator, the function exp can calculate the exponential online of a number.

    To calculate the exponential of a number, just enter the number and to apply the function exp. Thus, for calculating the exponential of the number 0, you must enter exp(`0`) or directly 0, if the button exp already appears, the result 1 is returned.

  3. Derivative of exponential
  4. The derivative of the exponential is equal to exp(x).

  5. Calculate chain rule of derivatives with exponential
  6. If u is a differentiable function, the chain rule of derivatives with the exponential function and the function u is calculated using the following formula : `(exp(u(x)))'=u'(x)*exp(u(x))`, the derivative calculator can perform this type of calculation as this example shows calculating the derivative of exp(4x+3).

  7. Antiderivative of exponential
  8. The antiderivative of the exponential is equal to exp(x).

  9. Limits of exponential
    • The limits of the exponential exist at `-oo` and `+oo`:
    • The exponential function has a limit in `-oo` which is 0.
      • `lim_(x->-oo)exp(x)=0`
    • The exponential function has a limit in `+oo` which is `+oo`.
      • `lim_(x->+oo)exp(x)=+oo`

  10. Equation with exponential
  11. The calculator has a solver that allows him to solve a equation with exponential . The calculations for obtaining the results are detailed, so it will be possible to solve equations like `exp(x)=2` or like `exp(2*x+4)=3` or like `exp(x^2-1)=1` with the steps calculations.

Syntax :

exp(x), where x is a number.


Examples :


Derivative exponential :

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

The derivative of exp(x) is derivative(`exp(x)`)=`exp(x)`


Antiderivative exponential :

Antiderivative calculator allows to calculate an antiderivative of exponential function.

An antiderivative of exp(x) is antiderivative(`exp(x)`)=`exp(x)`


Limit exponential :

The limit calculator allows the calculation of limits of the exponential function.

The limit of exp(x) is limit(`exp(x)`)


Inverse function exponential :

The inverse function of exponential is the napierian logarithm function noted ln.



Graphic exponential :

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


Calculate online with exp (exponential)
See also
List of related calculators :
  • Exponential : exp. The function exp calculates online the exponential of a number.
  • Logarithmic expansion : expand_log. The calculator makes it possible to obtain the logarithmic expansion of an expression.
  • Napierian logarithm : ln. The ln calculator allows to calculate online the natural logarithm of a number.
  • Logarithm : log. The log function calculates the logarithm of a number online.
  • 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.
  • Absolute value : abs. The abs function calculates online the absolute value of a number.
  • Arccosine : arccos. The arccos function allows the calculation of the arc cosine of a number. The arccos 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 arcsin function is the inverse function of the sine function.
  • Arctangent : arctan. The arctan function allows the calculation of the arctan of a number. The arctan function is the inverse functions of the tangent function.
  • Cosine : cos. The cos trigonometric function calculates the cos of an angle in radians, degrees or gradians.
  • Cosecant : cosec. The trigonometric function sec allows to calculate the secant of an angle expressed in radians, degrees, or grades.
  • Cotangent : cotan. The cotan trigonometric function to calculate the cotan of an angle in radians, degrees or gradians.
  • Cube root : cube_root. The cube_root function calculates online the cube root of a number.
  • Secant : sec. The trigonometric function sec allows to calculate the secant of an angle expressed in radians, degrees, or grades.
  • Sine : sin. The sin trigonometric function to calculate the sin of an angle in radians, degrees or gradians.
  • Square root : sqrt. The sqrt function allows to calculate the square root of a number in exact form.
  • Tangent : tan. The tan trigonometric function to calculate the tan of an angle in radians, degrees or gradians.

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