0x66a8d586

Let \(x_i\) be a coordinate map corresponding to a local chart \((U, \varphi)\). Then for \(p \in U\)

\begin{equation*} \Bigl(\frac{\partial }{\partial x_i}\Bigr)_p(f)=\Bigl[\frac{\partial (f\circ \varphi^{-1})}{\partial x_i} \Bigr]_{\varphi(p)} \end{equation*}

defines a tangent vector .