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# Derivative

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Derivative has both a mathematical and a financial? meaning.

Mathematically, 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 tangent to the graph of the function at that point.

Suppose we wish to find the derivative 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 (in print, more commonly denoted Δx) we can calculate f(a + dx). An approximation to the slope of the tangent to the curve is given by (f(a + dx) - f(a)) / dx, which is to say it is the change in f divided by the change in x. The smaller the value dx, the better approximation.

Mathematically, we define the derivative, denoted f´(a), to be the mathematical limit of this ratio as dx tends to zero. Functions which possess a derivative are said to be differentiable.

Financially, a derivative is an investment?, the value of which is based on, or derived from, another source (often called an underlying security?). Common examples of derivatives are option?s or future?s. The price of a futures contract is derived from the price of the underlying commodity?, e.g. corn?.

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Last edited July 26, 2001 9:28 pm (diff)
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