You could use the Quotient Rule, or rewrite this fraction without the negative exponent in the denominator.

$\frac{d}{dx}(y^{3}-3xy)=\frac{d}{dx}(3^{y})$

$y'=\frac{-3y}{\ln(3)\cdot e^{y}+3x-3y^{2}}=\frac{dy}{dx}$

Before differentiating, rewrite $g(t)$ with a fractional exponent.