Differentiating both sides of
<em>xy</em> = 99
with respect to <em>t</em> yields
<em>x</em> d<em>y</em>/d<em>t</em> + <em>y</em> d<em>x</em>/d<em>t</em> = 0
When <em>x</em> = 11, we have
11<em>y</em> = 99 ==> <em>y</em> = 9
and we're given that d<em>y</em>/d<em>t</em> = -4 at this point, which means
11 (-4) + 9 d<em>x</em>/d<em>t</em> = 0 ==> d<em>x</em>/d<em>t</em> = 44/9