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Derivative/Notations

From AoPSWiki

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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