I understand that for the parametric equations
$\begin{align*}x&=f(t)\\ y&=g(t)\end{align*}$
If $F(x)$ is the function with parameter removed then \displaystyle F'(x) = \frac{\text{d}y}{\text{d}t}\big/\frac{\text{d}x}{\text{d}t}
But the procedure for taking the second derivative is just described as " replace $y$ with dy/dx " to get
$\frac{\text{d}^2y}{\text{d}x^2}=\frac{\text{d}}{\text{d}x}\left(\frac{\text{d}y}{\text{d}x}\right)=\frac{\left[\frac{\text{d}}{\text{d}t}\left(\frac{\text{d}y}{\text{d}t}\right)\right]}{\left(\frac{\text{d}x}{\text{d}t}\right)}$
I don't understand the justification for this step. Not at all.
But that's all my book says on the matter then it launches in to plugging things in to this formula, and it seems to work well enough, but I don't know why.
I often find answers about question on differentials are beyond my level, I'd really like to get this, it'd mean a lot to me if someone could break it down.