Let $M$ a differentiable manifold and $p \in M$. Consider $(U;x_1, \dots, x_n)$ a coordinated system around $p$. $\{dx_\phi\}_\phi$ with $\phi \in \cal{P}(\{1, \dots n\})$, $dx_\phi=dx_{i1} \wedge \dots \wedge dx_{in}$ if $\phi=i1, \dots,in$ and $dx_\phi=1$ if $\phi=\emptyset$ isa basis of $\wedge T^*M$. Consider $a_\phi \in \cal{C}^\infty(U)$.
How can I show that $p \longrightarrow \sum da_\phi|_p \wedge dx_\phi|_p$ is differentiable?