Difference between revisions of "Derivative Command"

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<noinclude>{{Manual Page|version=4.0}}[[Category:Manual (official)|{{PAGENAME}}]]</noinclude>
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|function}}
{{command|function}}
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;Derivative( <Function> )
; Derivative[<Function>]: Returns the derivative of the function.  
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:Returns the derivative of the function with respect to the main variable.
; Derivative[<Function>, <Number n>]: Returns the ''n''<sup>th</sup> derivative of the function.
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:{{example|1=<code><nowiki>Derivative(x^3 + x^2 + x)</nowiki></code> yields ''3x² + 2x + 1''.}}
; Derivative[<Curve>]: Returns the derivative of the curve.  
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;Derivative( <Function>, <Number> )
:{{Note|It only works for parametric curves.}}
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:Returns the ''n''<sup>th</sup> derivative of the function with respect to the main variable, whereupon ''n'' equals <Number>.
; Derivative[<Curve>, <Number n>]: Returns the ''n''<sup>th</sup> derivative of the curve.  
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:{{example|1=<code><nowiki>Derivative(x^3 + x^2 + x, 2)</nowiki></code> yields ''6x + 2''.}}
:{{Note|It only works for parametric curves.}}
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;Derivative( <Function>, <Variable> )
 
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:Returns the partial derivative of the function with respect to the given variable.
{{Note| 1=You can use <code>f'(x)</code> instead of <code>Derivative[f]</code>, or <code>f<nowiki>''</nowiki>(x)</code> instead of <code>Derivative[f, 2]</code>, and so on.}}
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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> )
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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=<code><nowiki>Derivative(x^3 + 3x y, x, 2)</nowiki></code> yields ''6x''.}}
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;Derivative( <Curve> )
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:Returns the derivative of the curve.  
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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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:{{note| 1=This only works for parametric curves.}}
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;Derivative( <Curve>, <Number> )
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:Returns the ''n''<sup>th</sup> derivative of the curve, whereupon ''n'' equals <Number>.
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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==
In [[CAS View]] only following syntax is supported:
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;Derivative( <Expression> )
 
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:Returns derivative of an expression with respect to the main variable.
; Derivative[<Function f> or <Expression f>]: Returns derivative of ''f'' with respect to ''x''.
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:{{example|1=<code><nowiki>Derivative(x^2)</nowiki></code> yields ''2x''.}}
; Derivative[<Function f> or <Expression f>, <Variable a>]: Returns derivative of ''f'' with respect to ''a''.
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;Derivative( <Expression>, <Variable> )
; Derivative[<Function f> or <Expression f>, <Variable a>, <Number n>]: Returns the ''n''<sup>th</sup> derivative of ''f'' with respect to ''a''.
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:Returns derivative of an expression with respect to the given variable.
 
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:{{example| 1=<code><nowiki>Derivative(a x^3, a)</nowiki></code> yields ''''.}}
: {{Example|1=&nbsp;
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;Derivative( <Expression>, <Variable>, <Number> )
:* <code>Derivative[x^2]</code> gives you "2x". <br />  <br /> Assuming you've declared ''f'' as <code>f(x):=a*x^3</code>
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:Returns the ''n''<sup>th</sup> derivative of an expression with respect to the given variable, whereupon ''n'' equals <Number>.
:* <code>Derivative[f(x)];</code> gives you ''3a x²''.
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:{{examples| 1=<div>
:* <code>Derivative[f(x), a];</code> gives you ''x³''.
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:*<code><nowiki>Derivative(y x^3, x, 2)</nowiki></code> yields ''6xy''.
:* <code>Derivative[f(x), x, 2];</code> gives you ''6a x''.}}
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:*<code><nowiki>Derivative(x³ + 3x y, x, 2)</nowiki></code> yields ''6x''.</div>}}

Latest revision as of 08:05, 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 .
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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