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GeoGebra Manual
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- Derivative( <Function> )
- Returns the derivative of the function with respect to the main variable.
- 예:
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>.
- 예:
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.
- 예:
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>.
- 예:
Derivative(x^3 + 3x y, x, 2)
yields 6x. - Derivative( <Curve> )
- Returns the derivative of the curve.
- 예:
Derivative(Curve(cos(t), t sin(t), t, 0, π))
yields curve x = -sin(t), y = sin(t) + t cos(t). - 노트: This only works for parametric curves.
- Derivative( <Curve>, <Number> )
- Returns the nth derivative of the curve, whereupon n equals <Number>.
- 예:
Derivative(Curve(cos(t), t sin(t), t, 0, π), 2)
yields curve x = -cos(t), y = 2cos(t) - t sin(t). - 노트: This only works for parametric curves.
노트: 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.
- 예:
Derivative(x^2)
yields 2x. - Derivative( <Expression>, <Variable> )
- Returns derivative of an expression with respect to the given variable.
- 예:
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>.
- 예:
Derivative(y x^3, x, 2)
yields 6xy.Derivative(x³ + 3x y, x, 2)
yields 6x.