# 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 , the derivitave is n.

Note that when we take the derivative of any polynomial , 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 is

The following pages provide additional information on derivatives.

- Notations
- Formal definition of the derivative
- Formulas

## See also

*This article is a stub. Help us out by expanding it.*