Definition:Differential of Mapping/Real-Valued Function

Notation
Substituting $\map {\d x_i} {x; h} = h_i$ for $i = 1, 2, \ldots, n$, the following notation emerges:
 * $\ds \d f := \sum_{i \mathop = 1}^n \frac {\partial f} {\partial x_i} \rd x_i = \frac {\partial f} {\partial x_1} \rd x_1 + \frac {\partial f} {\partial x_2} \rd x_2 + \cdots + \frac {\partial f} {\partial x_n} \rd x_n$