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THIS QUESTION WAS MIGRATED PROM PHYSICS SE, SO THE ANSWERS MAY NOT BE APPLICABLE TO MATHEMATICS

$\left(\frac{\partial f}{\partial x}\right)_y$ means to differentiate $f(x,y)$ with respect to $x$, while holding $y$ constant. Would it be possible to write this simply as $\frac{\partial f(x)}{\partial x}$ instead, or are there any other alternatives in use?

Frank Vel
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  • What about $\frac{\partial f(x,y)}{\partial x}$? – Farcher Oct 07 '16 at 11:32
  • @Farcher couldn't that imply that $y$ is still a variable? – Frank Vel Oct 07 '16 at 11:33
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    The fact that you have used a partial d, $(\partial)$ immediately tells you which of the variables are to be considered as not changing. $\frac{\partial f}{\partial x}$ is also fine and saves time when writing. – Farcher Oct 07 '16 at 11:40

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Writing $\frac{\partial f(x)}{\partial x}$ is misleading because it suggests that $f$ does not depend on $y$. This can be harmful because in the reader's mind, this means $\frac{\partial f}{\partial y}=0$. This is why @Farcher's suggestion to write $\frac{\partial f(x,y)}{\partial x}$ is a better option. but once again, this is likely to imply that $f$ does not depend on anything else ($z$...). So unless you are sure to list all possible variables, I would recommend to stick to the standard $\left(\frac{\partial f}{\partial x}\right)_y$.

Tom-Tom
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    If that's the amount of characters to typeset in $\TeX$ that bothers you, you can create your macro \newcommand\ddd[3]{\left(\frac{\partial #1}{\partial #2}\right)_{#3}} and just use \ddd{f}{x}{y} for $\left(\frac{\partial f}{\partial x}\right)_{y}$. – Tom-Tom Oct 07 '16 at 11:44
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    For a mathematician, $\Bigl(\dfrac{\partial f}{\partial x}\Bigr)_y$ is not at all standard, as it means $\dfrac{\partial f}{\partial x}$ evaluated at $y$! – Bernard Oct 07 '16 at 23:06
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    @Bernard It seems this question was migrated here for no reason. I specifically asked on Physics SE because the notation is only used in physics. – Frank Vel Oct 08 '16 at 13:04
  • @Frank Vel: I see. You physicists have indeed special notations… ;o) – Bernard Oct 08 '16 at 13:12