# Difference between revisions of "Derivative Command"

From GeoGebra Manual

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; Derivative[<Function>]: Returns the derivative of the function. | ; Derivative[<Function>]: Returns the derivative of the function. | ||

; Derivative[<Function>, <Number n>]: Returns the ''n''<sup>th</sup> derivative of the function. | ; Derivative[<Function>, <Number n>]: Returns the ''n''<sup>th</sup> derivative of the function. | ||

− | ; Derivative[<Curve>]: {{ | + | ; Derivative[<Curve>]: Returns the derivative of the curve. |

− | ; Derivative[<Curve>, <Number n>]: {{ | + | :{{Note|It only works for parametric curves.}} |

+ | ; Derivative[<Curve>, <Number n>]: Returns the ''n''<sup>th</sup> derivative of the curve. | ||

+ | :{{Note|It only works for parametric curves.}} | ||

{{Note| 1=You can use <code>f'(x)</code> instead of <code>Derivative[f]</code>, or <code>f<nowiki>''</nowiki>(x)</code> instead of <code>Derivative[f, 2]</code>, and so on.}} | {{Note| 1=You can use <code>f'(x)</code> instead of <code>Derivative[f]</code>, or <code>f<nowiki>''</nowiki>(x)</code> instead of <code>Derivative[f, 2]</code>, and so on.}} |

## Revision as of 10:11, 4 August 2011

- Derivative[<Function>]
- Returns the derivative of the function.
- Derivative[<Function>, <Number n>]
- Returns the
*n*^{th}derivative of the function. - 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[<Function f> or <Expression f>]
- Returns derivative of
*f*with respect to*x*. - Derivative[<Function f> or <Expression f>, <Variable a>]
- Returns derivative of
*f*with respect to*a*. - Derivative[<Function f> or <Expression f>, <Variable a>, <Number n>]
- Returns the
*n*^{th}derivative of*f*with respect to*a*.

**Example:**`Derivative[x^2]`

gives you "2x".

Assuming you've declared*f*as`f(x):=a*x^3`

`Derivative[f(x)];`

gives you*3a x²*.`Derivative[f(x), a];`

gives you*x³*.`Derivative[f(x), x, 2];`

gives you*6a x*.