Definition:Partial Derivative

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:


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

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