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 nth 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 nth 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 nth 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 nth 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.