Mathematical interpretation of pressure (gradient)

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I'm having some problem with the following.

Usually, the pressure of some mass on an area A is defined by $$P=\frac{F}{A}$$ where $F$ is the force of the mass exerted due to gravity. However, here http://en.wikipedia.org/wiki/Force#Continuum_mechanics

we find the identity $$-\nabla P =\frac{F}{V}$$ where $V$ is some volume (and probably an area is also allowed here). However, I was trying to see this identity with the Gradient theorem but failed. So essentially my question is: where does the gradient come from?