The Definition and Limit Method

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The derivative of a function expresses its rate of change with respect to an independent variable. The derivative is also the slope of the tangent line to the curve. As you might recall. Many students start out differentiating with the Limit Method. The Limit Method utilizes the definition of a derivative of a function. The Limit Method, as seen below, is imperative because some problems may not work or may take longer with the differentiation rules.

                               lim    f(x + c) - f(x)
                            c-->0            c
      (Where c denotes a small distance on the x-axis usually written as the lower case delta sign next to an x)