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
-
The limits of the exponential exist at `-oo` and `+oo`:
- The exponential function has a limit in `-oo` which is 0.
- The exponential function has a limit in `+oo` which is `+oo`.
- `lim_(x->-oo)exp(x)=0`
- `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.
- 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.
- Usual numerical functions calculator : usual_functions. This calculator lets you apply most standard numerical functions to a number: cos, sin, tan, arctan, cotan, arccos, arcsin, exp, ln, log, sh, ch, th, coth, sec, sqrt, cube_root.
- 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.