Answer
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Work Step by Step
Having a differentiable function $f$ of two variables, the directional derivative $\nabla_u f(x_0, y_0)$ at a point $P(x_0, y_0)$ represents the rate of change of a function with respect to distance in the direction of a unit vector $\mathbf{u}$. Geometrically, $\nabla_u f(x_0, y_0)$ can be interpreted as the slope of the surface $z = f(x, y)$ at a point $(x_0, y_0, f(x_0, y_0))$ in the direction of the unit vector $\mathbf{u}$. This means that it represents the slope of the line going through $P(x_0, y_0)$ and parallel to $\mathbf{u}$
