Wikipedia 10K Redux by Reagle from Starling archive. Bugs abound!!!

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The Derivative of a [[Function]] at a point is a measure of the  rate at which that function is changing as one of the [[Variable]]s changes.  This corresponds to the slope of the graph of the function at that point.

Intuitively, suppose we wish to find the derivate of a suitably smooth [[Function]], f(x) say, at the point x=a.  If we increase x by a small amount, which we'll call dx (or more accurately delta x) we can  calculate f(x + dx), and an approximation to the slope is given my (f(a+dx)-f(a)) / dx.   The smaller the value dx, the better approximation.  Mathematically, we define the derivative, denoted f'(a), to be the limit of the ratio as dx tends to zero.