The function exp calculates online the exponential of a number.

Exponential function

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

Calculation of the exponential

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.

Derivative of exponential

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

Calculate chain rule of derivatives with exponential

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).

Antiderivative of exponential

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

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`

Equation with exponential

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 :

• exp(`0`)`=1`
• exp(`i*pi/3`)`=1/2+i*sqrt(3)/2`
• exp(`i*x`)`=cos(x)+i*sin(x)`

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.