Derivative Command

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.