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.  Note that not every function has a derivative.
 
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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== How to Find the Derivative ==
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For any constant, the derivative is 0.
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For any monomial <math>nx</math>, the derivitave is n.
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Note that when we take the derivative of any polynomial <math>a_nx^n+a_{n-1}x^{n-1}+...+a_1x+a_0</math>, we can take the derivative of each addend and then add these to find the derivative of the polynomial.
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The chain rule states that the derivative of any <math>ax^n</math> is <math>anx^{n-1}</math>
  
 
The following pages provide additional information on derivatives.
 
The following pages provide additional information on derivatives.

Revision as of 22:58, 9 September 2006

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.


How to Find the Derivative

For any constant, the derivative is 0.

For any monomial $nx$, the derivitave is n.

Note that when we take the derivative of any polynomial $a_nx^n+a_{n-1}x^{n-1}+...+a_1x+a_0$, we can take the derivative of each addend and then add these to find the derivative of the polynomial.

The chain rule states that the derivative of any $ax^n$ is $anx^{n-1}$

The following pages provide additional information on derivatives.

See also

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