Differential of Real-Valued Function/Examples

Examples of Differentials of Real-Valued Functions

Function of 2 Variables

Let $f: \R^2 \to \R$ be a real-valued function of $2$ variables.

Let $z = \map f {x, y}$ for all $\tuple {x, y} \in \R^2$.

Then the differential of $z$ is given by:

$\d z := \dfrac {\partial f} {\partial x} \d x + \dfrac {\partial f} {\partial y} \d y$