Consider the parametric equations $x=x(t),y=y(t)$, then the parametric derivative is $$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}, \text{ provided }\frac{dx}{dt}\not=0.$$
My question is: Is the derivative not defined at $\frac{dx}{dt}=0$? Especially if I write $x(t)=cos(t),y(t)=cos(t)^2$, then is $y'(x)$ not defined at $x=0$?