# Derivative Command

From GeoGebra Manual

- Derivative( <Function> )
- Returns the derivative of the function with respect to the main variable.
**Example:**`Derivative(x^3 + x^2 + x)`

yields*3x² + 2x + 1*.

- Derivative( <Function>, <Number> )
- Returns the
*n*^{th}derivative of the function with respect to the main variable, whereupon*n*equals <Number>. **Example:**`Derivative(x^3 + x^2 + x, 2)`

yields*6x + 2*.

- Derivative( <Function>, <Variable> )
- Returns the partial derivative of the function with respect to the given variable.
**Example:**`Derivative(x^3 y^2 + y^2 + xy, y)`

yields*2x³y + x + 2y*.

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

yields*6x*.

- Derivative( <Curve> )
- Returns the derivative of the curve.
**Example:**`Derivative(Curve(cos(t), t sin(t), t, 0, π))`

yields curve*x = -sin(t), y = sin(t) + t cos(t)*.

**Note:**This only works for parametric curves.- Derivative( <Curve>, <Number> )
- Returns the
*n*^{th}derivative of the curve, whereupon*n*equals <Number>. **Example:**`Derivative(Curve(cos(t), t sin(t), t, 0, π), 2)`

yields curve*x = -cos(t), y = 2cos(t) - t sin(t)*.

**Note:**This 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

- Derivative( <Expression> )
- Returns derivative of an expression with respect to the main variable.
**Example:**`Derivative(x^2)`

yields*2x*.

- Derivative( <Expression>, <Variable> )
- Returns derivative of an expression with respect to the given variable.
**Example:**`Derivative(a x^3, a)`

yields*x³*.

- Derivative( <Expression>, <Variable>, <Number> )
- Returns the
*n*^{th}derivative of an expression with respect to the given variable, whereupon*n*equals <Number>. **Examples:**`Derivative(y x^3, x, 2)`

yields*6xy*.`Derivative(x³ + 3x y, x, 2)`

yields*6x*.