exponential

Exponential : How to use it?

The function exp calculates online the exponential of a number.

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.

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

limits of the exponential

$-oo$

$+oo$

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.