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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.   The '''derivative''' of a [[function]] is defined as the instantaneous [[rate]] of change of the function with respect to one of the [[variable]]s. 
   
−  == Notation ==
 +  * [[Derivative/Notations  Notations]] 
−   +  * [[Derivative/Mathematical definition  Mathematical definition]] 
−  The following are commonly recognized notations for expressing the derivative of a function.
 +  * [[Derivative/Formulas  Formulas]] 
−   
−  { class="wikitable" style="textalign:center; margin: 1em auto 1em auto; height:600px; width:300px"
 
−   colspan="2"  '''Euler's notation'''
 
−  
 
−   First derivative  <math>D_xf(x)</math> or <math>Du</math>
 
−  
 
−   Second derivative  <math>D_x^2f(x)</math> or <math>D^2u</math>
 
−  
 
−   Third derivative  <math>D_x^3f(x)</math> or <math>D^3u</math>
 
−    
−   <math>n</math>th derivative  <math>D_x^nf(x)</math> or <math>D^nu</math>
 
−  
 
−   colspan="2"  '''Lagrange's notation'''
 
−  
 
−   First derivative  <math>f'(x)</math>
 
−  
 
−   Second derivative  <math>f''(x)</math>
 
−  
 
−   Third derivative  <math>f'''(x)</math>
 
−  
 
−   <math>n</math>th derivative  <math>f^{(n)}(x)</math>
 
−  
 
−   colspan="2"  '''Leibniz's notation'''
 
−  
 
−   First derivative  <math>\frac{dy}{dx}</math>
 
−  
 
−   Second derivative  <math>\frac{d^2y}{dx^2}</math>
 
−  
 
−   <math>n</math>th derivative  <math>\frac{d^ny}{dx^n}</math>
 
−  
 
−   colspan="2"  '''Newton's notation'''
 
−  
 
−   First derivative  <math>\dot{x}</math>
 
−  
 
−   Second derivative  <math>\ddot{x}</math>
 
−  }  
   
 == See also ==   == See also == 
 * [[Calculus]]   * [[Calculus]] 
 * [[Integral]]   * [[Integral]] 
Revision as of 21:42, 30 July 2006
The derivative of a function is defined as the instantaneous rate of change of the function with respect to one of the variables.
See also