Let $\displaystyle x_1,...,x_n: M \rightarrow R $ be functions on a manifold which form a local coordinate system on some region. Show that every differential form on this region can be written uniquely in the form

$\displaystyle w^k = \sum_{i_1<...<i_k} a_{i_1,...i_k}(\bf{x})dx_{1_i} \wedge .. \wedge dx_{1_k} $

Any ideas?