y)$, then $d\vec F$
    approximates how much the wind vector changes between the two
    points (i.e., how much the output of $\vec F$ changes). The
    derivative $D\vec F$ relates a small change in inputs (moving a
    small distance) to changes the outputs (the wind vector). We
    can then ask questions like: what direction should I move so
    that the velocity of the wind goes down? What direction should
    I move so that the wind blows more in a northern direction? If
    I walk in this direction, 