For the given functions, $($a$)$ express $\frac{dw}{dt}$ as a function of t $,$ both by using the Chain Rule and by expressing w in terms of $t$ and differentiating directly with respect to $t.$ Then $($b$)$ evaluate $\frac{dw}{dt}$ at the given value of $t.$

$w=\frac{x}{z}+\frac{y}{z},x=si{n}^{2}t,y=co{s}^{2}t,z=\frac{1}{8t}$;$t=5$

a$.$ Which of the equations represents an initial step of expressing $\frac{dw}{dt}$ using the Chain Rule?

A$.\frac{dw}{dt}=\frac{si{n}^{2}t}{8t}+\frac{co{s}^{2}t}{8t}$

B$.\frac{dw}{dt}=(-\frac{1}{z})(2sintcost)-(\frac{1}{z})(-2costsint)-(-\frac{x}{z^2}-\frac{y}{z^2})(-\frac{1}{8t^2})$

c$.\frac{dw}{dt}=(\frac{1}{z})(2sintcost)+(\frac{1}{z})(-2costsint)+(-\frac{x}{z^2}-\frac{y}{z^2})(-\frac{1}{8t^2})$

D$.\frac{dw}{dt}=\frac{si{n}^{2}t}{\frac{1}{8}t}+\frac{co{s}^{2}t}{\frac{1}{8}t}$

What equation represents $w$ in terms of $t?$

$w=$