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). A function z = f ( x, y ) z = f ( x, y ) has two partial derivatives: ∂ z / ∂ x ∂ z / ∂ x and ∂ z / ∂ y. In Partial Derivatives we introduced the partial derivative.

4.6.3 Explain the significance of the gradient vector with regard to direction of change along a surface.4.6.2 Determine the gradient vector of a given real-valued function.4.6.1 Determine the directional derivative in a given direction for a function of two variables.