# How does function $x_i \rightarrow f(x_1,x_2, …, x_i, …, x_n)$ Lipschitz imply existence of partial derivatives?

How does function $$x_i \rightarrow f(x_1,x_2, ..., x_i, ..., x_n)$$ Lipschitz imply existence of partial derivatives?

Particularly, is there a way to write this in such form that expresses component-wise differentiability?