# 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

# 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.

#### 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)
• 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 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.
• 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 cotangent 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 sine 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 tangent of an angle in radians, degrees or gradians.

Real functions | Complex numbers