Answer
$\frac{dy}{dt}$ = $(1+tan^{4}(\frac{t}{12}))^{2}$$(tan^{3}(\frac{t}{12}))$($sec^{2}(\frac{t}{12})$)
Work Step by Step
$y$ = $(1+tan^{4}(\frac{t}{12}))^{3}$
$\frac{dy}{dt}$ = $\frac{d}{dt}$$(1+tan^{4}(\frac{t}{12}))^{3}$
$\frac{dy}{dt}$ = $3(1+tan^{4}(\frac{t}{12}))^{2}$ $\frac{d}{dt}$$(1+tan^{4}(\frac{t}{12}))$
$\frac{dy}{dt}$ = $3(1+tan^{4}(\frac{t}{12}))^{2}$$(4tan^{3}(\frac{t}{12}))$ $\frac{d}{dt}$$(tan(\frac{t}{12}))$
$\frac{dy}{dt}$ = $3(1+tan^{4}(\frac{t}{12}))^{2}$$(4tan^{3}(\frac{t}{12}))$$sec^{2}(\frac{t}{12})$ $\frac{d}{dt}$$(\frac{t}{12})$
$\frac{dy}{dt}$ = $3(1+tan^{4}(\frac{t}{12}))^{2}$$(4tan^{3}(\frac{t}{12}))$($sec^{2}(\frac{t}{12})$)$(\frac{1}{12})$
$\frac{dy}{dt}$ = $(1+tan^{4}(\frac{t}{12}))^{2}$$(tan^{3}(\frac{t}{12}))$($sec^{2}(\frac{t}{12})$)
