Answer
$\frac{dy}{dt}$ = [$6tan(sin^{3}t)$][$sec^{2}(sin^{3}t)$][$sin^{2}t$][$cost$]
Work Step by Step
$y$ = $tan^{2}(sin^{3}t)$
$\frac{dy}{dt}$ = $2tan(sin^{3}t)$ $\frac{d}{dt}$$tan(sin^{3}t)$
$\frac{dy}{dt}$ = [$2tan(sin^{3}t)$][$sec^{2}(sin^{3}t)$] $\frac{d}{dt}$$(sin^{3}t)$
$\frac{dy}{dt}$ = [$2tan(sin^{3}t)$][$sec^{2}(sin^{3}t)$][$3sin^{2}t$] $\frac{d}{dt}$$(sint)$
$\frac{dy}{dt}$ = [$6tan(sin^{3}t)$][$sec^{2}(sin^{3}t)$][$sin^{2}t$][$cost$]
