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Derivative

Revision as of 19:16, 30 July 2006 by Joml88 (talk | contribs) (Notation)

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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