A way to write derivatives There are many notations when it comes to derivatives such as $f'(x)$ and $\frac{dy}{dx}$. As of the moment, I can't find a reference that uses $dy/dx$ instead of $\frac{dy}{dx}$.
Is it acceptable to write $\frac{dy}{dx}$ as $dy/dx$ or not?
Yes, absolutely. Writing $\frac{dy}{dx}$ as $dy/dx$ is much the same as writing $\frac{3}{5}$ as $3/5$. There is no mathematical difference between the two notations—only a typographical one.
Writing $\frac{dy}{dx}$ or $dy/dx$ is a matter of choice, mathematical speaking they are both ratios, so I can even write as $[ dy : dx ]$
But when compiling a good math text, in textbooks or some type-settings, it's better to write as $\frac{dy}{dx}$ because it looks more like function than variable
Also consider when we want to write higher derivatives
$$\frac{d^7y}{dx^7}$$
$$d^7y/dx^7$$
vote to choose