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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. |
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| − | == 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="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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| − | |-
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| − | | Third derivative || <math>D_x^3f(x)</math> or <math>D^3u</math>
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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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| − | |} | |
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| | == See also == | | == See also == |
| | * [[Calculus]] | | * [[Calculus]] |
| | * [[Integral]] | | * [[Integral]] |
