Given a smooth function $f:\mathbb R^n\rightarrow \mathbb R$, can I expand it at $a\in \mathbb R^n$so that 

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> $f(x)=f(a)+\sum(x\_i-a)g\_i(x)$ where $g\_i$ are smooth functions with $g\_i(a)=\frac {\partial f}{\partial x\_i}(a)$?
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If so, I would like to see some reference for(or direct here) the proof.