# Derivative

The derivative of a function $$f(x)$$ is the limit, if any, of the expression
$\frac{f(x+\delta)-f(x)}{\delta}$
as $$\delta$$ tends to zero.

The value of the derivative at $$y$$ is typically witten as one of
$\frac{\mathrm{d}f}{\mathrm{d}x}\bigg|_y \;=\; \frac{\mathrm{d}f}{\mathrm{d}x}(y) \;=\; \overset{\cdot}{f}(y) \;=\; f^\prime(y)$
The derivative represents the rate of change of the function with reprect to its argument or, equivalently if we plot the function as a graph its tangent, or slope.

By repeating the process $$n$$ times we recover higher order derivatives, typically written as one of
$\frac{\mathrm{d}^nf}{\mathrm{d}x^n}\bigg|_y \;=\; \frac{\mathrm{d}^nf}{\mathrm{d}x^n}(y) \;=\; f^{(n)}(y)$

### Gallimaufry

 AKCalc ECMA Endarkenment Turning Sixteen

This site requires HTML5, CSS 2.1 and JavaScript 5 and has been tested with

 Chrome 26+ Firefox 20+ Internet Explorer 9+