To see the derivative via zooming one needs to magnify BOTH the DOMAIN and the RANGE -- at equal rates. This requires to “subtract the drift” first.
Move the left lever - now coupled with the right lever to see the convergence to a linear field. Drag the lens to see different derivatives at different points.
Note the additional link to linear algebra -- pastel colors show the eigenspaces (and sign of the eigenvalues) at points where these are real...