In Partial Derivatives we introduced the partial derivative. A function [latex]z=f(x,y)[/latex] has two partial derivatives: [latex]\partial{z} {/} \partial{x}[/latex] and [latex]\partial{z} {/} \partial{y}[/latex]. These derivatives correspond to each of the independent variables and can be interpreted as instantaneous rates of change (that is, as slopes of a tangent line). For example, [latex]\partial{z} {/} \partial{x}[/latex] represents the slope of a tangent line passing through a given point on the surface defined by [latex]z=f(x,y)[/latex], assuming the tangent line is parallel to the [latex]x[/latex]-axis. Similarly, [latex]\partial{z} {/} \partial{y}[/latex] represents the slope of the tangent line parallel to the [latex]y[/latex]-axis. Now we consider the possibility of a tangent line parallel to neither axis.