exponential
- exp(`0`)`=1`
- exp(`i*pi/3`)`=1/2+i*sqrt(3)/2`
- exp(`i*x`)`=cos(x)+i*sin(x)`
Exponential : 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
- Derivative of exponential
- Calculate chain rule of derivatives with exponential
- Antiderivative of exponential
- Limits of exponential
- The exponential function has a limit in `-oo` which is 0.
- The exponential function has a limit in `+oo` which is `+oo`.
- Equation with 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.
The derivative of the exponential is equal to exp(x).
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).
The antiderivative of the exponential is equal to exp(x).
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The limits of the exponential exist at `-oo` and `+oo`:
- `lim_(x->-oo)exp(x)=0`
- `lim_(x->+oo)exp(x)=+oo`
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.
- 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.