derivative(form, u) vs. derivative(form, u, du)

Question

The third argument du in the derivative(...) method is optional, cf.
http://fenicsproject.org/documentation/dolfin/dev/python/programmers-reference/fem/formmanipulations/derivative.html.

What's the actual difference between

J = derivative(form, u)

and

J = derivative(form, u, du)

if both return the Jacobian?

In the Cahn-Hilliard demo, du is used somewhat strangely in that neither of dc, dmu = split(du) is used in the code,

Comments

The link to the doc of derivative is broken.

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Fixed. (In preview the link was alright, but the final representation decided to include the full stop at the end of the sentence to the URL.)

Answer 1

The direction of derivative becomes a new argument of a resulting form - TrialFunction, TestFunction or another argument according to the rank of the original form by default. You can override this logic by supplying a new argument, du here. The Cahn-Hilliard demo would work also without specifying this.