Difference between revisions of "Derivative"

(Notation)
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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.
  
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| colspan="2" | '''Euler's notation'''
 
| colspan="2" | '''Euler's notation'''
 
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| Second derivative || <math>\ddot{x}</math>
 
| Second derivative || <math>\ddot{x}</math>
 
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== See also ==
 
== See also ==
 
* [[Calculus]]
 
* [[Calculus]]
 
* [[Integral]]
 
* [[Integral]]

Revision as of 20:16, 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 $D_xf(x)$ or $Du$
Second derivative $D_x^2f(x)$ or $D^2u$
Third derivative $D_x^3f(x)$ or $D^3u$
$n$th derivative $D_x^nf(x)$ or $D^nu$
Lagrange's notation
First derivative $f'(x)$
Second derivative $f''(x)$
Third derivative $f'''(x)$
$n$th derivative $f^{(n)}(x)$
Leibniz's notation
First derivative $\frac{dy}{dx}$
Second derivative $\frac{d^2y}{dx^2}$
$n$th derivative $\frac{d^ny}{dx^n}$
Newton's notation
First derivative $\dot{x}$
Second derivative $\ddot{x}$

See also

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