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%%
Show that the {\em general formula}
is

\begin{equation}\label{eq:faa-de-bruno}
D^n_xw =
\sum_{0\le j\le n}
\sum_{\scriptstyle k_1+k_2+\cdots+k_n=j
\atop {\scriptstyle k_1+2k_2+\cdots+nk_n=n
\atop  {\scriptstyle k_1,k_2,\ldots,k_n\ge0
}}}
D^j_u w \frac{n! 
{(D^1_x u)}^{k_1}
\cdots {(D^n_x u)}^{k_n}
}
{k_1!{(1!)}^{k_1} \cdots k_n!{(n!)}^{k_n}} 
\end{equation}

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