\begin{definition}[Definition:Partial Derivative/Real Analysis/Open Set]
Let $U\subset\R^n$ be an open set.
Let $f : U \to \R$ be a real-valued function.
Let $f$ be differentiable in $U$.
The '''$i$th partial derivative (function) of $f$ with respect to $x_i$''' is the real-valued function which sends each $x\in U$ to the $i$th partial derivative at $x$.
Category:Definitions/Partial Differentiation
\end{definition}