# Derivative Command

From GeoGebra Manual

Revision as of 13:10, 21 October 2011 by Christina.biermair (talk | contribs)

- 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 given 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 given 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 the given variable*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 the given variable*a*. **Example:**`Derivative[a x^3, x, 2]`

yields*6 a x*.