To do this, we first find $\frac{dy}{dt}$ and $\frac{dx}{dt}$.
Given $y = 2at$, we have $\frac{dy}{dt} = 2a$.
Given $x = at^2$, we have $\frac{dx}{dt} = 2at$.
Then, we take $\frac{dy}{dt}$ divided by $\frac{dx}{dt}$ to get $\frac{dy}{dx}$:
\[\frac{dy}{dx} =
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