Answer
$$
\frac{d y}{d x}= \frac{2t}{e^t}
$$
and at $t=1$, we have
$$
\frac{d y}{d x}= \frac{2}{e}.
$$
Work Step by Step
Since $x=e^t$ and $y=t^2$, then we have
$$
\frac{d y}{d x}= \frac{y^{\prime}}{x^{\prime}}=\frac{2t}{e^t}
$$
and at $t=1$, we have
$$
\frac{d y}{d x}= \frac{2}{e}.
$$
