Can FEniCS take a derivative of an Expression?

I have defined a Function U and an Expression V as follows:

import fenics as fe
nelements = 8
degree = 2
m = fe.UnitIntervalMesh(nelements)
DE = fe.FiniteElement('DG', m.ufl_cell(), degree)
DS = fe.FunctionSpace(m, DE)
U = fe.Function(DS)
wU = fe.TestFunction(DS)
Vstr = '-beta*log(alpha + U)'
V = fe.Expression(Vstr, degree = degree, alpha=1, beta=1, U=U)

This works exactly as I hoped it would. V depends on U. For instance, if I do this:

U.vector()[1] = 1

then plot V, I find it has changed. Also,

dxx = fe.Measure('dx', m)
fe.assemble(V*dxx)

gives the entirely plausible result -0.014440566261665524.

Now I want to compute the derivative of the integral of V with respect to the degrees of freedom of U. So, with consummate naivete, I tried this:

fe.derivative(V*dxx, U)
dV = fe.assemble(fe.derivative(V*dxx, U))
dV.array()

array([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
        0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.])

It sort of works, in that I, now getting a vector result, but this is not the answer I was hoping for... Is there a way to get the differentiation to propagate through the Expression?