Difference between revisions of "Derivative Command"
From GeoGebra Manual
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|function}} | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|function}} | ||
− | ;Derivative | + | ;Derivative( <Function> ) |
:Returns the derivative of the function with respect to the main variable. | :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''.}} | :{{example|1=<code><nowiki>Derivative[x^3 + x^2 + x]</nowiki></code> yields ''3x² + 2x + 1''.}} | ||
− | ;Derivative | + | ;Derivative( <Function>, <Number> ) |
:Returns the ''n''<sup>th</sup> derivative of the function with respect to the main variable, whereupon ''n'' equals <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''.}} | :{{example|1=<code><nowiki>Derivative[x^3 + x^2 + x, 2]</nowiki></code> yields ''6x + 2''.}} | ||
− | ;Derivative | + | ;Derivative( <Function>, <Variable> ) |
:Returns the partial derivative of the function with respect to the given 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''.}} | :{{example|1=<code><nowiki>Derivative[x^3 y^2 + y^2 + xy, y]</nowiki></code> yields ''2x³y + x + 2y''.}} | ||
− | ;Derivative | + | ;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>. | :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''.}} | :{{example|1=<code><nowiki>Derivative[x^3 + 3x y, x, 2]</nowiki></code> yields ''6x''.}} | ||
− | ;Derivative | + | ;Derivative( <Curve> ) |
:Returns the derivative of the 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)''.}} | :{{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.}} | :{{note| 1=This only works for parametric curves.}} | ||
− | ;Derivative | + | ;Derivative( <Curve>, <Number> ) |
:Returns the ''n''<sup>th</sup> derivative of the curve, whereupon ''n'' equals <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)''.}} | :{{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)''.}} | ||
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{{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.}} | {{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== | ==CAS Syntax== | ||
− | ;Derivative | + | ;Derivative( <Expression> ) |
:Returns derivative of an expression with respect to the main variable. | :Returns derivative of an expression with respect to the main variable. | ||
:{{example|1=<code><nowiki>Derivative[x^2]</nowiki></code> yields ''2x''.}} | :{{example|1=<code><nowiki>Derivative[x^2]</nowiki></code> yields ''2x''.}} | ||
− | ;Derivative | + | ;Derivative( <Expression>, <Variable> ) |
:Returns derivative of an expression with respect to the given 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''.}} | :{{example| 1=<code><nowiki>Derivative[a x^3, a]</nowiki></code> yields ''x³''.}} | ||
− | ;Derivative | + | ;Derivative( <Expression>, <Variable>, <Number> ) |
:Returns the ''n''<sup>th</sup> derivative of an expression with respect to the given variable, whereupon ''n'' equals <Number>. | :Returns the ''n''<sup>th</sup> derivative of an expression with respect to the given variable, whereupon ''n'' equals <Number>. | ||
:{{examples| 1=<div> | :{{examples| 1=<div> | ||
:*<code><nowiki>Derivative[y x^3, x, 2]</nowiki></code> yields ''6xy''. | :*<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>}} | :*<code><nowiki>Derivative[x³ + 3x y, x, 2]</nowiki></code> yields ''6x''.</div>}} |
Revision as of 17:16, 7 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.