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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?

soupless
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2 Answers2

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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.

Joe
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  • What if it is $\dfrac{d^{2}u}{dx,dy}$? Do I write it as $(d^{2}u)/(dx,dy)$? – soupless Mar 18 '21 at 16:14
  • It's not clear to me what $\frac{d^2u}{dxdy}$ even means. Regardless, it is always acceptable to indicate division using a slash instead of a fraction bar. Even though $dy/dx$ is not really a fraction, we adopt the same typographical convention as we do for the quotient of two numbers. – Joe Mar 18 '21 at 16:17
  • What I mean is like $\dfrac{d}{dy}\left(\dfrac{du}{dx}\right)$. – soupless Mar 18 '21 at 16:18
  • @soupless: For more complicated expressions, it is better style to use a horizontal bar than a slash. But the meaning of those expressions is the same. – Joe Mar 18 '21 at 16:20
  • @ancientmathematician Can you please leave it here? I really find it useful. – soupless Mar 18 '21 at 16:44
  • @soupless: To summarise, there is no problem with writing $\frac{dy}{dx}$ as $dy/dx$, so long as you remember that $dy/dx$ is not a ratio—rather, it is the limit of a ratio. If you want more information about that, then see here. – Joe Mar 18 '21 at 16:51
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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

Aderinsola Joshua
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    As cited by @Joe, $\frac{dy}{dx}$ is not a ratio, though in some cases, it can be treated as if it is a ratio. – soupless Mar 18 '21 at 17:06