In Partial Derivatives we introduced the partial derivative. A function $z=f(x,y)$ has two partial derivatives: $\partial{z} {/} \partial{x}$ and $\partial{z} {/} \partial{y}$. 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, $\partial{z} {/} \partial{x}$ represents the slope of a tangent line passing through a given point on the surface defined by $z=f(x,y)$, assuming the tangent line is parallel to the $x$-axis. Similarly, $\partial{z} {/} \partial{y}$ represents the slope of the tangent line parallel to the $y$-axis. Now we consider the possibility of a tangent line parallel to neither axis.