Answer
$$
\frac{d y}{d x}=6t^2-1
$$
and at $(0,2)$, we have
$$
\frac{d y}{d x}=5.
$$
Work Step by Step
Since $x=\ln t$ and $y=3t^2- t$, then we have
$$
\frac{d y}{d x}=\frac{d y / d t}{d x / d t}=\frac{y^{\prime}(t)}{x^{\prime}(t)}=\frac{6t-1}{1/t} =6t^2-1
$$
and at $(0,2)$, we have $\ln t =0$, that is $t=1$
$$
\frac{d y}{d x}= 6-1=5.
$$
