Solution
= Solution
For the <parametric curve>, $dx/dt=e^t\ne0$ and $dy/dt=\cos t$. Therefore $dy/dx=e^{-t}\cos t$. The condition $x=e^t=1$ gives $t=0$, so
$$
\boxed{\left.\frac{dy}{dx}\right|_{x=1}=1.}
$$
= Solution
For the <parametric curve>, $dx/dt=e^t\ne0$ and $dy/dt=\cos t$. Therefore $dy/dx=e^{-t}\cos t$. The condition $x=e^t=1$ gives $t=0$, so
$$
\boxed{\left.\frac{dy}{dx}\right|_{x=1}=1.}
$$