Derivative

The derivative of a function is a second function showing the rate of change of the dependent variable compared to the independent variable. It can be thought of as a graph of the slope of the function from which it is derived. The process of finding a derivative is called differentiation. The derivative of y with respect to x (denoted as y') is equal to
:y' = \lim _{\Delta x \rightarrow 0} \frac{\Delta y}{\Delta x} = \frac{\mathrm{d}x}{\mathrm{d}y}\,
The inverse of differentiation is integration.
==Multivariable extensions==
For multivariable scalar fields, either a gradient (a vector field representing the direction of greatest change) or directional derivative (a scalar representing the rate of change in a particular direction) can be taken. The two equivalents to derivation over a scalar field are divergence and curl. 
==Derivatives in physics==
:x'(t) = v(t)
:v'(t) = a(t)
:W'(d) = F(d)
:W'(t) = P(t)
:\nabla \cdot V = \vec{E}
:f(x)=f'(X)
:
==See also==
*Table of derivatives
*Integration
*Derivative on Math wiki
Category:Mathematical operations