I'm trying to understand the meaning behind the leibniz notations when taking the derivative of a parametric equation.
Say we have $x=f(t)$ and $y=g(t)$
Why does the derivative of this equal $\frac{\frac{dy}{dt}}{\frac{dx}{dt}}$? I guess what I'm trying to ask is, how does the "derivative of $y$ with respect to $t$" over "derivative of $x$ with respect to $t$" equal "derivative of $y$ with respect to $x$"? And what happens when I want to take a second derivative of a parametric equation? How would that work?