Difference between revisions of "Derivative Command"
From GeoGebra Manual
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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[ <Expression f> ] | ;Derivative[ <Expression f> ] | ||
:Returns derivative of ''f'' with respect to the main variable. | :Returns derivative of ''f'' with respect to the main variable. | ||
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;Derivative[ <Expression f>, <Variable a> ] | ;Derivative[ <Expression f>, <Variable a> ] | ||
:Returns derivative of ''f'' with respect to the given variable ''a''. | :Returns derivative of ''f'' with respect to the given variable ''a''. | ||
| − | :{{example| 1=<div><code><nowiki>Derivative[ | + | :{{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 f>, <Variable a>, <Number n> ] | ||
:Returns the ''n''<sup>th</sup> derivative of ''f'' with respect to the given variable ''a''. | :Returns the ''n''<sup>th</sup> derivative of ''f'' with respect to the given variable ''a''. | ||
| − | :{{ | + | :{{examples| 1=<div> |
| + | ::<code><nowiki>Derivative[y x^3, x, 2]</nowiki></code> yields ''6xy''. | ||
| + | ::<code><nowiki>Derivative[x³ + 3xy, x, 2]</nowiki></code> yields ''6x''.</div>}} | ||
Revision as of 14:46, 19 December 2012
- Derivative[ <Function> ]
- Returns the derivative of the function with respect to the main variable.
- Derivative[ <Function>, <Number n> ]
- 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 n> ]
- 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 n> ]
- 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 f> ]
- Returns derivative of f with respect to the main variable.
- Example:
Derivative[x^2]yields 2 x.
- Example:
Derivative[t^3]yields 3 t2.
- Derivative[ <Expression f>, <Variable a> ]
- Returns derivative of f with respect to the given variable a.
- Example:
Derivative[y x^3, y]yields x3.
- Derivative[ <Expression f>, <Variable a>, <Number n> ]
- Returns the nth derivative of f with respect to the given variable a.
- Examples:
Derivative[y x^3, x, 2]yields 6xy.Derivative[x³ + 3xy, x, 2]yields 6x.
