Difference between revisions of "Derivative Command"

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:{{example| 1=<div><code><nowiki>Derivative[t^3]</nowiki></code> yields ''3  t<sup>2</sup>''.</div>}}
 
:{{example| 1=<div><code><nowiki>Derivative[t^3]</nowiki></code> yields ''3  t<sup>2</sup>''.</div>}}
 
;Derivative[ <Expression f>, <Variable a> ]
 
;Derivative[ <Expression f>, <Variable a> ]
:Returns derivative of ''f'' with respect to ''a''.
+
:Returns derivative of ''f'' with respect to the given variable ''a''.
 
:{{example| 1=<div><code><nowiki>Derivative[a x^3, a]</nowiki></code> yields ''x<sup>3</sup>''.</div>}}
 
:{{example| 1=<div><code><nowiki>Derivative[a x^3, a]</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 ''a''.
+
:Returns the ''n''<sup>th</sup> derivative of ''f'' with respect to the given variable ''a''.
 
:{{example| 1=<div><code><nowiki>Derivative[a x^3, x, 2]</nowiki></code> yields ''6 a x''.</div>}}
 
:{{example| 1=<div><code><nowiki>Derivative[a x^3, x, 2]</nowiki></code> yields ''6 a x''.</div>}}

Revision as of 13:10, 21 October 2011


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

In CAS View only following syntax is supported:

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[a x^3, a] yields x3.
Derivative[ <Expression f>, <Variable a>, <Number n> ]
Returns the nth derivative of f with respect to the given variable a.
Example:
Derivative[a x^3, x, 2] yields 6 a x.
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