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

$w=-3x^{2}7y^2,x=costy=sintt=\frac{}{2}$

Express $\frac{dw}{dt}$ as a function of t$.$

$\frac{dw}{dt}=$