Answer
$\dfrac{da}{dt} = \dfrac{4t^3-6a^2}{4a^3-12at}$
Work Step by Step
In order to derivate this function you have to apply implicit differentation method.
Then derivate the whole equation. Rember the put a' every time you derivate a
$4a^3a'-4t^3-12aa't+6a^2=0$
Solve for a' and you have the answer
$a'(4a^3-12at)=4t^3-6a^2$
$a' = \dfrac{4t^3-6a^2}{4a^3-12at}$
