Derivative Command

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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 .
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.
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