$(a)$ Let $z=x^2+y^2,$ where $x=2t^3$ and $y=e^t.$ Determine $\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{t}}.$

$(7$ marks$)$

$(b)Ifyis$ a differentiable function $ofx$ such that

$x^2+4x^{2}y-3xy+y^2=0$

$By$ using implicit differentiation, find $\frac{dy}{dx}.$

$(3$ marks$)$