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Difference between revisions of "Derivative"

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The '''derivative''' of a [[function]] is defined as the instantaneous [[rate]] of change of the function with respect to one of the [[variable]]s.
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The '''derivative''' of a [[function]] is defined as the instantaneous [[rate]] of change of the function with respect to one of the [[variable]]s.  Note that not every function has a derivative.
  
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== Notation ==
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The following pages provide additional information on derivatives.
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* [[Derivative/Definition | Formal definition]] of the derivative and examples of applications
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The following are commonly recognized notations for expressing the derivative of a function.
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* [[Derivative/Formulas | Formulas]]
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{| class="wikitable" style="text-align:center; margin: 1em auto 1em auto; height:600px; width:300px"
 
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| colspan="2" | '''Euler's notation'''
 
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|-
 
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| First derivative || <math>D_xf(x)</math> or <math>Du</math>
 
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|-
 
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| Second derivative || <math>D_x^2f(x)</math> or <math>D^2u</math>
 
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| Third derivative || <math>D_x^3f(x)</math> or <math>D^3u</math>
 
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|-
 
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| <math>n</math>th derivative || <math>D_x^nf(x)</math> or <math>D^nu</math>
 
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|-
 
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| colspan="2" | '''Lagrange's notation'''
 
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|-
 
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| First derivative || <math>f'(x)</math>
 
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|-
 
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| Second derivative || <math>f''(x)</math>
 
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|-
 
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| Third derivative || <math>f'''(x)</math>
 
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|-
 
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| <math>n</math>th derivative || <math>f^{(n)}(x)</math>
 
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|-
 
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| colspan="2" | '''Leibniz's notation'''
 
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|-
 
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| First derivative || <math>\frac{dy}{dx}</math>
 
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|-
 
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| Second derivative || <math>\frac{d^2y}{dx^2}</math>
 
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|-
 
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| <math>n</math>th derivative || <math>\frac{d^ny}{dx^n}</math>
 
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|-
 
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| colspan="2" | '''Newton's notation'''
 
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|-
 
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| First derivative || <math>\dot{x}</math>
 
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|-
 
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| Second derivative || <math>\ddot{x}</math>
 
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|}
 
  
 
== See also ==
 
== See also ==
 
* [[Calculus]]
 
* [[Calculus]]
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* [[Differentiation Rules]]
 
* [[Integral]]
 
* [[Integral]]
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* [[Chain Rule]]
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[[Category:Calculus]]

Latest revision as of 18:26, 3 March 2010

The derivative of a function is defined as the instantaneous rate of change of the function with respect to one of the variables. Note that not every function has a derivative.

The following pages provide additional information on derivatives.

See also

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