Difference between revisions of "Derivative Command"
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− | <noinclude>{{Manual Page}} | + | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|function}} |
− | ; Derivative | + | ;Derivative( <Function> ) |
− | ; Derivative | + | :Returns the derivative of the function with respect to the main variable. |
− | + | :{{example|1=<code><nowiki>Derivative(x^3 + x^2 + x)</nowiki></code> yields ''3x² + 2x + 1''.}} | |
− | ''' | + | ;Derivative( <Function>, <Number> ) |
+ | :Returns the ''n''<sup>th</sup> derivative of the function with respect to the main variable, whereupon ''n'' equals <Number>. | ||
+ | :{{example|1=<code><nowiki>Derivative(x^3 + x^2 + x, 2)</nowiki></code> yields ''6x + 2''.}} | ||
+ | ;Derivative( <Function>, <Variable> ) | ||
+ | :Returns the partial derivative of the function with respect to the given variable. | ||
+ | :{{example|1=<code><nowiki>Derivative(x^3 y^2 + y^2 + xy, y)</nowiki></code> yields ''2x³y + x + 2y''.}} | ||
+ | ;Derivative( <Function>, <Variable>, <Number> ) | ||
+ | :Returns the ''n''<sup>th</sup> partial derivative of the function with respect to the given variable, whereupon ''n'' equals <Number>. | ||
+ | :{{example|1=<code><nowiki>Derivative(x^3 + 3x y, x, 2)</nowiki></code> yields ''6x''.}} | ||
+ | ;Derivative( <Curve> ) | ||
+ | :Returns the derivative of the curve. | ||
+ | :{{example|1=<code><nowiki>Derivative(Curve(cos(t), t sin(t), t, 0, π))</nowiki></code> yields curve ''x = -sin(t), y = sin(t) + t cos(t)''.}} | ||
+ | :{{note| 1=This only works for parametric curves.}} | ||
+ | ;Derivative( <Curve>, <Number> ) | ||
+ | :Returns the ''n''<sup>th</sup> derivative of the curve, whereupon ''n'' equals <Number>. | ||
+ | :{{example|1=<code><nowiki>Derivative(Curve(cos(t), t sin(t), t, 0, π), 2)</nowiki></code> yields curve ''x = -cos(t), y = 2cos(t) - t sin(t)''.}} | ||
+ | :{{note| 1=This only works for parametric curves.}} | ||
+ | {{note| 1=You can use <code><nowiki>f'(x)</nowiki></code> instead of <code><nowiki>Derivative(f)</nowiki></code>, or <code><nowiki>f''(x)</nowiki></code> instead of <code><nowiki>Derivative(f, 2)</nowiki></code>, and so on.}} | ||
+ | ==CAS Syntax== | ||
+ | ;Derivative( <Expression> ) | ||
+ | :Returns derivative of an expression with respect to the main variable. | ||
+ | :{{example|1=<code><nowiki>Derivative(x^2)</nowiki></code> yields ''2x''.}} | ||
+ | ;Derivative( <Expression>, <Variable> ) | ||
+ | :Returns derivative of an expression with respect to the given variable. | ||
+ | :{{example| 1=<code><nowiki>Derivative(a x^3, a)</nowiki></code> yields ''x³''.}} | ||
+ | ;Derivative( <Expression>, <Variable>, <Number> ) | ||
+ | :Returns the ''n''<sup>th</sup> derivative of an expression with respect to the given variable, whereupon ''n'' equals <Number>. | ||
+ | :{{examples| 1=<div> | ||
+ | :*<code><nowiki>Derivative(y x^3, x, 2)</nowiki></code> yields ''6xy''. | ||
+ | :*<code><nowiki>Derivative(x³ + 3x y, x, 2)</nowiki></code> yields ''6x''.</div>}} |
Latest revision as of 09:05, 9 October 2017
- 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 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.