To do this, we can use the chain rule, which states that $\frac{dy}{dx} = \frac{dy}{dt} \cdot \frac{dt}{dx}$. We know that $y = t^{2}$ and $x = t^{3} + t$, so we can find $\frac{dy}{dt}$ and $\frac{dx}{dt}$:
\[\frac{dy}{dt} = 2t\]
\[\frac{dx}{dt} = 3t^{2} +
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