Definition:Partial Derivative

Given a function of multiple variables $$f(x_1, \dots, x_n) \ $$, the partial derivative with respect to $$x_i \ $$ is defined

$$\frac{\partial f}{\partial x_i} = \frac{dg}{dx_i} \ $$

where $$g(x_i) = f(x_1, \dots, x_i, \dots, x_n) \ $$, where all the $$x_j, j \neq i \ $$ are considered as constant.