Let $X\_1,\dots,X\_n$ be n vector fields on an open subset $U$ of a manifold of dimension $n$ Suppose that at $p\in U$, the vectors $(X\_1)\_p,\dots,(X\_n)\_p$ are linearly indipendent. would any one say in detail how I will show that there is a chart $(V,x^1,\dots,x^n)$ about $p$ such that $(X)\_p=(\partial/\partial x^i)\_p$ for all $i=1,\dots,n$, here I use superscript for coordinates like $x^1,\dots,x^n$