A raindrop falls on a point $f(x_o,y_o)$ of the surface $z=f(x,y)$.
How do I find the direction in which the raindrop will roll downhill, given that the trajectory of the raindrop until it hits on the surface is parallel to the $y-axis$ (the $y-axis$ being the "vertical" one)?
Will it roll in the direction of the steepest descent?