Total Differential
Table of Contents
1 Definition
The total differential (not to be confused with the total derivative) of a scalar function \( u(x, y, z) \) is defined as:
\[ du = \frac{\partial u}{\partial x}dx + \frac{\partial u}{\partial y}dy + \frac{\partial u}{\partial z}dz \]
With the natural extension to functions of more than 3 variables. It gives an insight on how \( u \) changes (\( du \)) with respect to small changes in \( x, y \text{ and } z \) given by \( dx, dy \text{ and } dz \) respectively.