$7\mathrm{.}9.$ Chain Rule. Use the chain rule to find:

$($a$)\frac{dz}{dt}$ when $z=x^2{y}^2,x=t^3,y=1t^2$

$($b$)\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{s}}$ and $\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{t}}$ when $z=x^2-3x^2{y}^2,x=s{e}^t,y=s{e}^{-t}$

$($c$)\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{s}}$ and $\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{t}}$ at $s=0,t=1$ when $z=x^{2}tan(2y),x=s^2{t}^2,y=2st$