How do you find the delta x and delta y on a graph?

The delta x and delta y (dx and dy) are the changes in x and in y. When you take the derivative you are provided with a ratio (rise over run) of these changes.

Take f(x)=3x^2 + 2x

Derivative: (dy/dx)=6x + 2

From this, you can solve for dx and dy algebraically.