# Difference between revisions of "Derivative"

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The following are commonly recognized notations for expressing the derivative of a function. | The following are commonly recognized notations for expressing the derivative of a function. | ||

− | {| class="wikitable" style="margin: 1em auto 1em auto | + | {| class="wikitable" style="text-align:center; margin: 1em auto 1em auto" |

− | | | + | | colspan="2" | '''Euler's notation''' |

− | |||

|- | |- | ||

− | | | + | | First derivative || <math>D_xf(x)</math> or <math>Du</math> |

|- | |- | ||

− | | || <math> | + | | Second derivative || <math>D_x^2f(x)</math> or <math>D^2u</math> |

|- | |- | ||

− | | || <math> | + | | Third derivative || <math>D_x^3f(x)</math> or <math>D^3u</math> |

|- | |- | ||

− | | || <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 20:12, 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.

## Notation

The following are commonly recognized notations for expressing the derivative of a function.

Euler's notation
| |

First derivative | or |

Second derivative | or |

Third derivative | or |

th derivative | or |

Lagrange's notation
| |

First derivative | |

Second derivative | |

Third derivative | |

th derivative | |

Leibniz's notation
| |

First derivative | |

Second derivative | |

th derivative | |

Newton's notation
| |

First derivative | |

Second derivative |