Suppose that you are skiing on a hillside with elevation

E$($x$,$ y$)=6$x $$ x$^2$ y$^2$

And you are at position $(1,2).$

$$

$($a$)$ What direction from $(1,2)$ gives the direction of steepest descent?$$ In other words, in what direction should you move from $(1,2)$ in order to go down the hill as fast as possibly, at least initially?$$ Your answer should be a $2$D vector.

$($b$)$ What is the rate of change in elevation if you ski in this direction $($of steepest descent$)?$