The derivative as a ratio

Question

As $$\frac{dy}{dx}= \lim_{∆x \to 0}\frac{∆y}{∆x}$$ then why $$\frac{dy}{dx}$$ is not a ratio ?

Answer 1

$\frac{dy}{dx}$ is simply (Leibnitz) notation for the derivative. It is a symbol, like $y'$, $y'(x)$, and so forth.