The cube_root function calculates online the cube root of a number.

Cube root function

The cube root of a real number x, is a number cubed equals x.

Calculation of the cube root

Online calculation of the cube root of a number

The function allows the online calculation of the cube root of a number.

For example, to calculate the cube root of the number 27, you must enter cube_root(`27`), after calculating the result `3` is returned.

For example, to perform the calculation of the cube root online of the number 8, enter cube_root(`8`), after calculating the value 2 is returned.

Some integer cube roots

The cube root function to determine the cube root of a number, here are some examples of special cubic roots given by the online calculator.

1. to calculate the cube root of 8, enter cube_root(`8`), the result is 2.
2. to calculate the cube root of 27, enter cube_root(`27`), the result is 3.
3. to calculate the cube root of 64, enter cube_root(`64`), the result is 4.
4. to calculate the cube root of 64, enter cube_root(`125`), the result is 5.

Derivative of cube root

The derivative of the cube root is equal to `1/(3*("cube_root"(x))^2)`=`1/(3*(root(3)(x))^2)`.

Antiderivative of cube root

The antiderivative of the cube root is equal to `3/4*(x)^(4/3)=3/4*(root(3)(x))^4`.

Limits of cube root

The limits of the cube root exist at `-oo` (minus infinity) and `+oo` (plus infinity):
• The cube root function has a limit in `-oo` which is `-oo`.
`lim_(x->-oo)root(3)(x)=-oo`
• The cube root function has a limit in `+oo` which is `+oo`.
`lim_(x->+oo)root(3)(x)=+oo`

Syntax :

cube_root(x), x is a number.

Examples :

cube_root(`27`), returns 3

Derivative cube root :

To differentiate function cube root online, it is possible to use the derivative calculator which allows the calculation of the derivative of the cube root function

The derivative of cube_root(x) is derivative(`"cube_root"(x)`)=`1/(3*("cube_root"(x))^2)`

Antiderivative cube root :

Antiderivative calculator allows to calculate an antiderivative of cube root function.

An antiderivative of cube_root(x) is antiderivative(`"cube_root"(x)`)=`3/4*(x)^(4/3)`

Limit cube root :

The limit calculator allows the calculation of limits of the cube root function.

The limit of cube_root(x) is limit(`"cube_root"(x)`)

Graphic cube root :

The graphing calculator is able to plot cube root function in its definition interval.