Consider $f(x,y)=\frac{2y}{x^2+y^2+4}.$

$($a$)$ Describe the level curves of $f$ and present a sketch.

$($b$)$ Use the notebook to plot the contour map for $-4x,y4$ with $12$ contours in total.

$($c$)$ Use the map to approximate $\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{y}}(0,1)$ and $\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{x}}(1,1)$