Definition:Partial Derivative

Definition
Given a function of multiple independent variables $f \left({x_1, \ldots, x_n}\right)$, the partial derivative with respect to $x_i$ is denoted and defined as:


 * $\dfrac{\partial f}{\partial x_i} = \dfrac{\mathrm d g}{\mathrm d x_i}$

where:
 * $g \left({x_i}\right) = f \left({x_1, \ldots, x_i, \dots, x_n}\right)$
 * $\dfrac{\mathrm d g}{\mathrm d x_i}$ is the derivative of $g$ with respect to $x_i$
 * all the $x_j, j \ne i$ are considered as constant.