derivative of a parametric function at a point

Question

I need to find the derivative of $$l\begin{cases} y=t\cdot \cos(t)\\ x=e^t-2t-1 \end{cases} $$ at $(0,0)$.

How do I approach this?

Thank you.

Answer 1

$$\frac{dy}{dx}\bigg|_{(0,0)}=\biggl(\frac{\frac{dy}{dt}}{\frac{dx}{dt}}\biggr)_{t=0}$$

Therefore $\frac{dy}{dx}\bigg|_{(0,0)}=\biggr(\frac{y'(t)}{x'(t)}\biggl)_{t=0}=\biggl(\frac{cos(t)-tsin(t)}{e^t-2}\biggr)_{t=0}=-1$