${}$
If a curve $C$ is defined parametrically by $x\=x\left(t\right)\,y\=y\left(t\right)$, the slope along the curve is given by
$\frac{d}{\mathrm{dx}}\stackrel{\^}{y}\left(x\right)\=\frac{\frac{\mathrm{dy}}{\mathrm{dt}}}{\frac{\mathrm{dx}}{\mathrm{dt}}}$
where $\stackrel{\^}{y}\left(x\right)\=y\left(t\left(x\right)\right)$. Unfortunately, nearly all texts fail to distinguish $\stackrel{\^}{y}$ from $y$, even though these are completely different functions. When this notational omission is made, the formula for the derivative of $\stackrel{\^}{y}$ assumes the perplexing form
$\frac{\mathrm{dy}}{\mathrm{dx}}\=\frac{y\prime \left(t\right)}{x\prime \left(t\right)}$
The most appropriate form for this formula would be the very explicit
$\frac{d}{\mathrm{dx}}\stackrel{\^}{y}\left(x\right)\=\genfrac{}{}{0ex}{}{\frac{y\prime \left(t\right)}{x\prime \left(t\right)}}{\phantom{x\=a}}|\genfrac{}{}{0ex}{}{\phantom{\mathrm{f(x)}}}{t\=t\left(x\right)}$
which follows from an application of the Chain and Inverse-Function rules for derivatives.
$\frac{d}{\mathrm{dx}}\stackrel{\^}{y}\left(x\right)\=\frac{d}{\mathrm{dx}}y\left(t\left(x\right)\right)\=\frac{\mathrm{dy}}{\mathrm{dt}}\frac{\mathrm{dt}}{\mathrm{dx}}\=\frac{\mathrm{dy}}{\mathrm{dt}}\left(\frac{1}{\frac{\mathrm{dx}}{\mathrm{dt}}}\right)\=\frac{\frac{\mathrm{dy}}{\mathrm{dt}}}{\frac{\mathrm{dx}}{\mathrm{dt}}}\=\frac{y\prime \left(t\right)}{x\prime \left(t\right)}$
The prime symbol used for differentiation represents an operator. By default, Maple interprets the prime to be the operator $\frac{d}{\mathrm{dx}}$. If the differentiation variable is other than $x$, then one way to have Maple re-interpret the prime is to include the independent variable explicitly. So, if using the prime to obtain the ratio of derivatives, include the appropriate independent variable as an explicit argument.
As a final caution, note that shortening the differentiation rule to something like $y\prime \=y\prime \/x\prime$ would befuddle even the most astute reader.