Understanding Differentiation - Sam Hart,1997 - hart@physics.arizona.edu
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The derivative is one of the most fundimental concepts of calculus 
(perhaps only superseded by the limit concept). The derivative has many 
equivalent definitions as to its function and interpretation. It is the 
tangential slope of the graph of a particular function at a point, the 
rate of change at an instant, and, when applied to vectors, the 
direction and magnitude of increase. We shall use the geometric 
interpretation of the derivative here, as we define it, because the ease 
of representing it as a tangential slope.

Take a linear function, something in the form of,   y(x) = Mx + B.

It is traditionally noted that in a linear function, the slope of the 
resultant line is equal to the rise over the run of the line. This can 
be computed by taking two arbitrary sets of points on the line, and 
computing the difference in the direction of travel (here, we’ll term 
the positive x values as our direction);

    Slope = Rise / Run  = Change in Vertical / Change in Horizontal
          = Change in Y / Change in X

Using the greek symbol delta, /\
                              ¯¯