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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 extensionsEdit

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 physicsEdit

x'(t) = v(t)
v'(t) = a(t)
W'(d) = F(d)
W'(t) = P(t)
\nabla \cdot V = \vec{E}

See alsoEdit

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