Faà di Bruno's formula gives an expression for the $n$th derivative of a composite function,
$\frac{d^n}{dt^n}f(g(t))$,
thereby generalising the chain rule. I was wondering whether there is also a formula available for
$\frac{d^n}{dt^n}f(t, g(t))$,
where $t$ also is an argument of $f$.