Difference between revisions of "Derivative Command"

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;Derivative[ <Function> ]
 
;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''.}}
 
;Derivative[ <Function>, <Number> ]
 
;Derivative[ <Function>, <Number> ]
 
:Returns the ''n''<sup>th</sup> derivative of the function with respect to the main variable.
 
:Returns the ''n''<sup>th</sup> derivative of the function with respect to the main variable.
 +
:{{example|1=<code><nowiki>Derivative[x^3 y^2 + y^2 + xy, y]</nowiki></code> yields ''2x³y + x + 2y''.}}
 
;Derivative[ <Function>, <Variable> ]
 
;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=<div><code><nowiki>Derivative[x³+3x y, x]</nowiki></code> yields ''3x²+3y''.</div>}}
+
:{{example|1=<code><nowiki>Derivative[x^3 + 3x y, x]</nowiki></code> yields ''3x² + 3y''.}}
 
;Derivative[ <Function>, <Variable>, <Number> ]
 
;Derivative[ <Function>, <Variable>, <Number> ]
 
:Returns the ''n''<sup>th</sup> partial derivative of the function with respect to the given variable.
 
:Returns the ''n''<sup>th</sup> partial derivative of the function with respect to the given variable.
−
:{{example|1=<div><code><nowiki>Derivative[x³+3x y, x, 2]</nowiki></code> yields ''6x''.</div>}}
+
:{{example|1=<code><nowiki>Derivative[x^3 + 3x y, x, 2]</nowiki></code> yields ''6x''.}}
 
;Derivative[ <Curve> ]
 
;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)''.}}
 
:{{note| 1=It only works for parametric curves.}}
 
:{{note| 1=It only works for parametric curves.}}
 
;Derivative[ <Curve>, <Number> ]
 
;Derivative[ <Curve>, <Number> ]
 
:Returns the ''n''<sup>th</sup> derivative of the curve.  
 
:Returns the ''n''<sup>th</sup> derivative of the curve.  
 +
:{{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=It only works for parametric curves.}}
 
:{{note| 1=It 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.}}
 
{{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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;Derivative[ <Expression> ]
 
;Derivative[ <Expression> ]
 
:Returns derivative of an expression with respect to the main variable.
 
:Returns derivative of an expression with respect to the main variable.
−
:{{examples|1=<div>
+
:{{examples|1=<code><nowiki>Derivative[x^2]</nowiki></code> yields ''2x''.}}
−
:*<code><nowiki>Derivative[x^2]</nowiki></code> yields ''2 x''.
 
−
:*<code><nowiki>Derivative[t^3]</nowiki></code> yields ''3  t<sup>2</sup>''.</div>}}
 
 
;Derivative[ <Expression>, <Variable> ]
 
;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=<div><code><nowiki>Derivative[y x^3, y]</nowiki></code> yields ''x<sup>3</sup>''.</div>}}
+
:{{example| 1=<div><code><nowiki>Derivative[y x^3, y]</nowiki></code> yields ''x³''.</div>}}
 
;Derivative[ <Expression>, <Variable>, <Number> ]
 
;Derivative[ <Expression>, <Variable>, <Number> ]
 
:Returns the ''n''<sup>th</sup> derivative of an expression with respect to the given variable.
 
:Returns the ''n''<sup>th</sup> derivative of an expression with respect to the given variable.
 
:{{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 + 3xy, x, 2]</nowiki></code> yields ''6x''.</div>}}
+
:*<code><nowiki>Derivative[x³ + 3x y, x, 2]</nowiki></code> yields ''6x''.</div>}}

Revision as of 13:33, 2 September 2013


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.
Example: Derivative[x^3 y^2 + y^2 + xy, y] yields 2x³y + x + 2y.
Derivative[ <Function>, <Variable> ]
Returns the partial derivative of the function with respect to the given variable.
Example: Derivative[x^3 + 3x y, x] yields 3x² + 3y.
Derivative[ <Function>, <Variable>, <Number> ]
Returns the nth partial derivative of the function with respect to the given variable.
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: It only works for parametric curves.
Derivative[ <Curve>, <Number> ]
Returns the nth derivative of the curve.
Example: Derivative[Curve[cos(t), t sin(t), t, 0, π], 2] yields curve x = -cos(t), y = 2cos(t) - t sin(t).
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 2x.
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 nth derivative of an expression with respect to the given variable.
Examples:
  • Derivative[y x^3, x, 2] yields 6xy.
  • Derivative[x³ + 3x y, x, 2] yields 6x.
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