Difference between revisions of "Derivative Command"

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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|function}}
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;Derivative( <Function> )
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;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.  
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;Derivative[ <Function>, <Number n> ]
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:{{example|1=<code><nowiki>Derivative(x^3 + x^2 + x)</nowiki></code> yields ''3x² + 2x + 1''.}}
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:Returns the ''n''<sup>th</sup> derivative of the function with respect to the main variable.
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;Derivative( <Function>, <Number> )
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;Derivative[ <Function>, <Variable> ]
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:Returns the ''n''<sup>th</sup> derivative of the function with respect to the main variable, whereupon ''n'' equals <Number>.
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:{{example|1=<code><nowiki>Derivative(x^3 + x^2 + x, 2)</nowiki></code> yields ''6x + 2''.}}
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;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.
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:{{example|1=<div><code><nowiki>Derivative[x³+3x y, x]</nowiki></code> yields ''3x²+3y''.</div>}}
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:{{example|1=<code><nowiki>Derivative(x^3 y^2 + y^2 + xy, y)</nowiki></code> yields ''2x³y + x + 2y''.}}
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;Derivative[ <Function>, <Variable>, <Number n> ]
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;Derivative( <Function>, <Variable>, <Number> )
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:Returns the ''n''<sup>th</sup> partial derivative of the function with respect to the given variable.
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:Returns the ''n''<sup>th</sup> partial derivative of the function with respect to the given variable, whereupon ''n'' equals <Number>.
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:{{example|1=<div><code><nowiki>Derivative[x³+3x y, x, 2]</nowiki></code> yields ''6x''.</div>}}
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:{{example|1=<code><nowiki>Derivative(x^3 + 3x y, x, 2)</nowiki></code> yields ''6x''.}}
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;Derivative[ <Curve> ]
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;Derivative( <Curve> )
 
:Returns the derivative of the curve.  
 
:Returns the derivative of the curve.  
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:{{note| 1=It only works for parametric curves.}}
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:{{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)''.}}
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;Derivative[ <Curve>, <Number n> ]
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:{{note| 1=This only works for parametric curves.}}
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:Returns the ''n''<sup>th</sup> derivative of the curve.  
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;Derivative( <Curve>, <Number> )
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:{{note| 1=It only works for parametric curves.}}
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:Returns the ''n''<sup>th</sup> derivative of the curve, whereupon ''n'' equals <Number>.
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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.}}
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:{{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=This only works for parametric curves.}}
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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.}}
 
==CAS Syntax==
 
==CAS Syntax==
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;Derivative[ <Expression f> ]
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;Derivative( <Expression> )
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:Returns derivative of ''f'' with respect to the main variable.
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:Returns derivative of an expression with respect to the main variable.
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:{{examples|1=<div>
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:{{example|1=<code><nowiki>Derivative(x^2)</nowiki></code> yields ''2x''.}}
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:*<code><nowiki>Derivative[x^2]</nowiki></code> yields ''2 x''.
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;Derivative( <Expression>, <Variable> )
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:*<code><nowiki>Derivative[t^3]</nowiki></code> yields ''3  t<sup>2</sup>''.</div>}}
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:Returns derivative of an expression with respect to the given variable.
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;Derivative[ <Expression f>, <Variable a> ]
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:{{example| 1=<code><nowiki>Derivative(a x^3, a)</nowiki></code> yields ''x³''.}}
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:Returns derivative of ''f'' with respect to the given variable ''a''.
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;Derivative( <Expression>, <Variable>, <Number> )
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:{{example| 1=<div><code><nowiki>Derivative[y x^3, y]</nowiki></code> yields ''x<sup>3</sup>''.</div>}}
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:Returns the ''n''<sup>th</sup> derivative of an expression with respect to the given variable, whereupon ''n'' equals <Number>.
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;Derivative[ <Expression f>, <Variable a>, <Number n> ]
 
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:Returns the ''n''<sup>th</sup> derivative of ''f'' with respect to the given variable ''a''.
 
 
:{{examples| 1=<div>
 
:{{examples| 1=<div>
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:*<code><nowiki>Derivative[y x^3, x, 2]</nowiki></code> yields ''6xy''.
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:*<code><nowiki>Derivative(y x^3, x, 2)</nowiki></code> yields ''6xy''.
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:*<code><nowiki>Derivative[x³ + 3xy, x, 2]</nowiki></code> yields ''6x''.</div>}}
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:*<code><nowiki>Derivative(x³ + 3x y, x, 2)</nowiki></code> yields ''6x''.</div>}}

Latest revision as of 09:05, 9 October 2017

Derivative

This article is about GeoGebra command.

Command Categories (All commands)


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.
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