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Differentiation is a method to compute the rate at which a dependent output y changes with respect to the change in the independent input x. This rate of change is called the derivative of y with respect to x. In more precise language, the dependence of y upon x means that y is a function of x. This functional relationship is often denoted y = f(x), where f denotes the function. If x and y are real numbers, and if the graph of y is plotted against x, the derivative measures the slope of this graph at each point.

The simplest case is when y is a linear function of x, meaning that the graph of y against x is a straight line. In this case, y = f(x) = m x + b, for real numbers m and b, and the slope m is given by

m = change in y/change in x = Dy/Dx

where the symbol D (the uppercase form of the Greek letter Delta) is an abbreviation for "change in." This formula is true because

y + Dy = f(x+ Dx) = m (x + Dx) + b = m x + b + m Dx = y + mDx.

It follows that Dy = m Dx. 28 October 2010

Comment0 0 13 November 2010

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