If x=e^t t and y=e^t t , then what is (d x)/(d y) at t=0 equal to?

$$\begin{aligned} & x=e^t \cdot \cos t \Rightarrow \frac{d x}{d t}=e^t \cdot \cos t-e^t \cdot \sin t \\ & y=e^t \cdot \sin t \Rightarrow \frac{d y}{d t}=e^t \cdot \sin t+e^t \cdot \cos t\end{aligned}$$\frac{d x}{d y}=\frac{\frac{d x}{d t}}{\frac{d y}{d t}}=\frac{e^t(\cos t-\sin t)}{e^t(\sin t+\cos t)}=\frac{\cos t-\sin t}{\sin t+\cos t}\left.\frac{d x}{d y}\right|_{t=0}=\frac{\cos 0-\sin 0}{\sin 0+\cos 0}=\frac{1-0}{0+1}=1$.