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(perhaps only superseded by the limit concept).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, /\
¯¯