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

Revision as of 10:15, 27 March 2013



Derivative[ <Function> ]
Returns the derivative of the function with respect to the main variable.
Derivative[ <Function>, <Number> ]
Returns the nth derivative of the function with respect to the main variable.
Derivative[ <Function>, <Variable> ]
Returns the partial derivative of the function with respect to the given variable.
Example:
Derivative[x³+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[x³+3x y, x, 2] yields 6x.
Derivative[ <Curve> ]
Returns the derivative of the curve.
Note: It only works for parametric curves.
Derivative[ <Curve>, <Number> ]
Returns the nth derivative of the curve.
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 2 x.
  • Derivative[t^3] yields 3 t2.
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 + 3xy, x, 2] yields 6x.
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