- The instantaneous velocity function for an object moving on a straight line;
- The function that gives the slope of the tangent line at a point on the graph of the function;
- The instantaneous rate of change function of a variable depending on an independent variable.

Establish a separate parallel axis for measuring the derivative as a number. The derivative as a number is transferred from the vector visualization of the derivative on the target line to a number on this third axis created to record the values of the derivative. An arrow is drawn from the number on the domain axis to the number on the third axis indicating the derivative as a function.

Adding more arrows
connecting values in the domain to the associated derivative values on
the third axis visualizes the derivative function further. This supports understanding of
the more traditional cartesian graph of the derivative where the
vertical axis is used ambiguously for both function and derivative
values even though these values have separate interpretations and units,

Martin Flashman, 2 August 2015, Created with GeoGebra GGB 1

GGB 2