Newton's divided differences identity

Question

Let $f$ be a function, $x_0,\ldots,x_n$ be distinct nodes and $f[x_0,\ldots,x_n]$ be the Newton's divided difference. Show that $$f[x_0,\ldots,x_n]=\sum_{l=0}^n\frac{f(x_l)}{\Pi_{m=0, m\neq l}^nx_l-x_m}$$