Derivative Command

Derivative( <Function> )

Returns the derivative of the function with respect to the main variable.

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>.

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.

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>.

Derivative(x^3 + 3x y, x, 2) yields 6x.

Derivative( <Curve> )

Returns the derivative of the curve.

Derivative(Curve(cos(t), t sin(t), t, 0, π)) yields curve x = -sin(t), y = sin(t) + t cos(t).

This only works for parametric curves.
Derivative( <Curve>, <Number> )

Returns the nth derivative of the curve, whereupon n equals <Number>.

Derivative(Curve(cos(t), t sin(t), t, 0, π), 2) yields curve x = -cos(t), y = 2cos(t) - t sin(t).

This only works for parametric curves.

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.

Derivative(x^2) yields 2x.

Derivative( <Expression>, <Variable> )

Returns derivative of an expression with respect to the given variable.

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.