Taking derivatives from mixed space

dolfinx
2

I think you need to use a dolfinx Function instead of a TrialFunction, the same way it is done in your dolfiny example.
This seems to be the equivalent of dolfiny that you are trying to make:

import ufl
from mpi4py import MPI
from dolfinx import fem, mesh
import basix
from basix.ufl import mixed_element

domain = mesh.create_box(
    MPI.COMM_WORLD,
    [[0.0, 0.0, 0.0], [1.0, 1.0, 1.0]],
    [1, 1, 1],
    mesh.CellType.hexahedron,
)

Ue = basix.ufl.element("P", domain.basix_cell(), 1, shape=(domain.geometry.dim,))
He = basix.ufl.quadrature_element(domain.basix_cell(), value_shape=(), degree=1)
Te = basix.ufl.blocked_element(
    He, shape=(domain.geometry.dim, domain.geometry.dim), symmetry=True
)

V_el = mixed_element([Ue, Te])
V = fem.functionspace(domain, V_el)

w = fem.Function(V)
u, P = ufl.split(w)
δw = ufl.TestFunction(V)

F = ufl.Identity(3) + ufl.grad(u)
δE = ufl.derivative(F, w, δw)

dx = ufl.Measure("dx", domain=domain)
form = (ufl.inner(δE, P)) * dx
forms = ufl.extract_blocks(form)
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