Answer
$\frac{dy}{dt}$ = [$-24cos^{3}(sec^{2}3t)$][$(sin(sec^{2}3t))$][$sec^{2}(3t)tan(3t)$]
Work Step by Step
$y$ = $cos^{4}(sec^{2}3t)$
$\frac{dy}{dt}$ = $\frac{d}{dt}$$cos^{4}(sec^{2}3t)$
$\frac{dy}{dt}$ = $4cos^{3}(sec^{2}3t)$ $\frac{d}{dt}$$(cos(sec^{2}3t))$
$\frac{dy}{dt}$ = $4cos^{3}(sec^{2}3t)$$(-sin(sec^{2}3t))$ $\frac{d}{dt}$$(sec^{2}3t)$
$\frac{dy}{dt}$ = [$4cos^{3}(sec^{2}3t)$][$(-sin(sec^{2}3t))$][$2sec(3t)$] $\frac{d}{dt}$$(sec(3t))$
$\frac{dy}{dt}$ = [$4cos^{3}(sec^{2}3t)$][$(-sin(sec^{2}3t))$][$2sec(3t)$][$sec(3t)tan(3t)$] $\frac{d}{dt}$$(3t)$
$\frac{dy}{dt}$ = [$4cos^{3}(sec^{2}3t)$][$(-sin(sec^{2}3t))$][$2sec(3t)$][$sec(3t)tan(3t)$]$(3)$
$\frac{dy}{dt}$ = [$-24cos^{3}(sec^{2}3t)$][$(sin(sec^{2}3t))$][$sec^{2}(3t)tan(3t)$]
