Differentiate $f$ and find the domain of $f$ if $f(x)=\ln\left(\ln\left(\ln(x+1)\right)\right)$.

$f'(x)=$
Domain:

Note: Enter the domain as an interval or union of disjoint intervals, using 'U' for union, 'inf' and '-inf' for $\infty$ and $-\infty$ if necessary.