A given function curve is shown in blue. The slope of this curve at the black point is shown in purple with the numerical value of the slope.
The red dot's y-coordinate is the value of the slope at this x-value.
If you grab the black dot and move it around, the red dot will trace out the shape of the given function's slope values, which is the shape of the function's derivative curve.
You can trace the derivatives of any function curve by double-clicking on the equation in the algebra window and editing the equation. (Click the 'Clear curves' button to clear the previous red derivative curve).
This could be used, for example, to allow students to see that a polynomial's derivative function is always a polynomial one degree lower than the original function's degree.
