Show that $\mathcal D_p(M)=\text{span}\left(\left.\frac{\partial }{\partial x^1}\right|_p,...,\left.\frac{\partial }{\partial x^n}\right|_p\right)$

Question

Let $M$ a manifold of dimension $n$. I have to show that $$\mathcal D_p(M)=\text{span}\left(\left.\frac{\partial }{\partial x^1}\right|_p,...,\left.\frac{\partial }{\partial x^n}\right|_p\right)$$ where $\mathcal D_p(M)$ is the set of the derivation of $M$ on $p$.

First, it's obvious that $\left.\frac{\partial }{\partial x^i}\right|_p\in \mathcal D_p(M)$ for all $i$. Now, to show that it span $\mathcal D_p(M)$, I have more problem. Any idea ?