  If E is a separable symmetric sequence space with trivial Boyd indices and
$\cC^E$ is the corresponding ideal of compact operators, then there exists a
$C^1$-function $f_E$, a self-adjoint element $W\in \cC^E$ and a densely defined
closed symmetric derivation $\delta$ on $\cC^E$ such that $W \in Dom \delta$,
but $f_E(W) \notin Dom \delta$.
