$($a$)$ Find $\frac{dy}{dx}$ expressed as a function of $t$ for the given the parametric equations:

$x=co{s}^5(t)$

$y=8si{n}^2(t)$

$\frac{dy}{dx}=$

$($b$)$ Find $\frac{d^{2}y}{d{x}^2}$ expressed as a function of $t.$

$\frac{d^{2}y}{d{x}^2}=$

$$

$($c$)$ Except for at the points where $\frac{dy}{dx}$ is undefined, is the curve concave up or concave down? $($Enter $\text{'}$up$\text{'}$ or 'down'$).$

Concave