Consider the following.

$w=x{y}^2+x^{2}z+y{z}^2,x=t^2,y=9t,z=9$

$(a)$ Find $\frac{dw}{dt}t.\frac{dw}{dt}=$

$(b)$ Find $\frac{dw}{dt}by$ converting $wto$ a function $oftt.\frac{dw}{dt}=$