  We prove weak and strong versions of the coarea formula and the chain rule
for distributional Jacobian determinants $Ju$ for functions $u$ in fractional
Sobolev spaces $W^{s,p}(\Omega)$, where $\Omega$ is a bounded domain in
$\mathbb{R}^n$ with smooth boundary. The weak forms of the formulae are proved
for the range $sp>n-1$, $s> \frac{n-1}{n}$, while the strong versions are
proved for the range $sp\geq n$, $s\geq \frac{n}{n+1}$. We also provide a chain
rule for distributional Jacobian determinants of H\"older functions and point
out its relation to two open problems in geometric analysis.
