Generalizing the chain rule
I'm not a mathematician but if the multiple composition $ f_1(f_2(f_3 \dots)))$ 
is equivalent to a sequence of single compositions $g_2(g_1)$, and another $g_3(g_2)$ and so forth.

The generalization looks reasonable for  $x, f_{1}, f_{2} \dots f_N \in \cal{R}$ and $f_i$ differentiable with no discontinuities.