# Difference between revisions of "Derivative Command"

From GeoGebra Manual

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{{command|cas=true|function}} | {{command|cas=true|function}} | ||

;Derivative[ <Function> ] | ;Derivative[ <Function> ] | ||

− | :Returns the derivative of the function. | + | :Returns the derivative of the function with respect to the main variable. |

;Derivative[ <Function>, <Number n> ] | ;Derivative[ <Function>, <Number n> ] | ||

− | :Returns the ''n''<sup>th</sup> derivative of the function. | + | :Returns the ''n''<sup>th</sup> derivative of the function with respect to the main variable. |

;Derivative[ <Function>, <Variable> ] | ;Derivative[ <Function>, <Variable> ] | ||

:Returns the partial derivative of the function with respect to the variable. | :Returns the partial derivative of the function with respect to the variable. | ||

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In [[CAS View]] only following syntax is supported: | In [[CAS View]] only following syntax is supported: | ||

;Derivative[ <Expression f> ] | ;Derivative[ <Expression f> ] | ||

− | :Returns derivative of ''f'' with respect to | + | :Returns derivative of ''f'' with respect to the main variable. |

:{{example|1=<div><code><nowiki>Derivative[x^2]</nowiki></code> yields ''2 x''.</div>}} | :{{example|1=<div><code><nowiki>Derivative[x^2]</nowiki></code> yields ''2 x''.</div>}} | ||

− | :{{example| 1=<div><code><nowiki>Derivative[ | + | :{{example| 1=<div><code><nowiki>Derivative[t^3]</nowiki></code> yields ''3 t<sup>2</sup>''.</div>}} |

;Derivative[ <Expression f>, <Variable a> ] | ;Derivative[ <Expression f>, <Variable a> ] | ||

:Returns derivative of ''f'' with respect to ''a''. | :Returns derivative of ''f'' with respect to ''a''. |

## Revision as of 11:33, 7 October 2011

- Derivative[ <Function> ]
- Returns the derivative of the function with respect to the main variable.
- Derivative[ <Function>, <Number n> ]
- Returns the
*n*^{th}derivative of the function with respect to the main variable. - Derivative[ <Function>, <Variable> ]
- Returns the partial derivative of the function with respect to the variable.
**Example:**`Derivative[x³+3x y, x]`

yields*3x²+3y*.

- Derivative[ <Function>, <Variable>, <Number n> ]
- Returns the
*n*^{th}partial derivative of the function with respect to the variable. **Example:**`Derivative[x³+3x y, x, 2]`

yields*6x*.

- Derivative[ <Curve> ]
- Returns the derivative of the curve.
**Note:**It only works for parametric curves.- Derivative[ <Curve>, <Number n> ]
- Returns the
*n*^{th}derivative of the curve. **Note:**It only works for parametric curves.

**Note:**You can use

`f'(x)`

instead of `Derivative[f]`

, or `f''(x)`

instead of `Derivative[f, 2]`

, and so on.## CAS Syntax

In CAS View only following syntax is supported:

- Derivative[ <Expression f> ]
- Returns derivative of
*f*with respect to the main variable. **Example:**`Derivative[x^2]`

yields*2 x*.

**Example:**`Derivative[t^3]`

yields*3 t*.^{2}

- Derivative[ <Expression f>, <Variable a> ]
- Returns derivative of
*f*with respect to*a*. **Example:**`Derivative[a x^3, a]`

yields*x*.^{3}

- Derivative[ <Expression f>, <Variable a>, <Number n> ]
- Returns the
*n*^{th}derivative of*f*with respect to*a*. **Example:**`Derivative[a x^3, x, 2]`

yields*6 a x*.