Difference between revisions of "Derivative"

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.

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

@@ Line 5: / Line 5: @@
 The following are commonly recognized notations for expressing the derivative of a function.
-{| class="wikitable" style="margin: 1em auto 1em auto;text-align:center"
+{| class="wikitable" style="text-align:center; margin: 1em auto 1em auto"
-|+ Common Notations for the Derivative of a Function
+| colspan="2" | '''Euler's notation'''
-! Name of Notation !! Example of Notation
 |-
-| Lagrange's notation || <math>f'(x)</math>
+| First derivative || <math>D_xf(x)</math> or <math>Du</math>
 |-
-| || <math>f''(x)</math>
+| Second derivative || <math>D_x^2f(x)</math> or <math>D^2u</math>
 |-
-| || <math>f'''(x)</math>
+| Third derivative || <math>D_x^3f(x)</math> or <math>D^3u</math>
 |-
-| || <math>\vdots</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 ==
 * [[Calculus]]
 * [[Integral]]