Derivative Command

Derivative[ <Function> ]

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

Derivative[ <Function>, <Number> ]

Returns the n^th derivative of the function with respect to the main variable.

Derivative[ <Function>, <Variable> ]

Returns the partial derivative of the function with respect to the given variable.

Example:

Derivative[x³+3x y, x] yields 3x²+3y.

Derivative[ <Function>, <Variable>, <Number> ]

Returns the n^th partial derivative of the function with respect to the given variable.

Example:

Derivative[x³+3x y, x, 2] yields 6x.

Derivative[ <Curve> ]

Returns the derivative of the curve.

Note: It only works for parametric curves.

Derivative[ <Curve>, <Number> ]

Returns the n^th derivative of the curve.

Note: It 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.

Examples:

• Derivative[x^2] yields 2 x.
• Derivative[t^3] yields 3 t².

Derivative[ <Expression>, <Variable> ]

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

Example:

Derivative[y x^3, y] yields x³.

Derivative[ <Expression>, <Variable>, <Number> ]

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

Examples:

• Derivative[y x^3, x, 2] yields 6xy.
• Derivative[x³ + 3xy, x, 2] yields 6x.