$($c$)$ Suppose that $z=x^2+y^2$ is a function of the independent variables $x$ and $y.$

$($i$)$ Find $\frac{dz}{dt}$ along the elliptical path $x=2cost,y=sint.$

$($ii$)$ What is $\frac{dz}{dt}$ at $t=\frac{}{4}?$