$4\mathrm{.}1$ Use partial derivatives to find $\frac{dy}{dx}$ if $xcosy=y{e}^x$

$4\mathrm{.}2$ Three students are stretching a giant band into an equilateral triangle.

If they are making the sides increase at a rate of $27c\frac{m}{s},$ how fast is the triangle $\text{'}s$ area increasing when the sides are $1,8m$ long?

Hint $($:$A=\frac{1}{2}absinC$