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In some German books, I see what I consider proper:

\int \mathrm d x

In other books, I just see this:

\int d x

Since everybody writes $\sin(x)$ instead of just $sin(x)$, I wonder why people write all operators upright, just not the “d”. Is it just that it is more typing (which is a lame excuse) or is there some really sound reason for that?

Please just don't say that it is “personal style”, since $sin(x)$ would clearly considered wrong.

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closed as off topic by diabonas, Martin Schröder, yo', egreg, Stefan Kottwitz Nov 4 '12 at 23:26

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It's a very long story. There's no right or wrong; surely that "d" is not a function in the same sense as sin. My opinion is that "dx" is a variable (precisely the same as "x", just in the dual space) and it's not "d" applied to "x". –  egreg Nov 4 '12 at 22:35
    
Trig functions have a convention, differentials do not. That's all. –  Ryan Reich Nov 4 '12 at 22:39
    
I have a problem with calling “dx” a variable, since “dy“ would be similar. But “ex“ would not be understood. This “d” is special. And how do you tell apart the differential “x” and the product of “d” (say a distance) with “x”? –  queueoverflow Nov 4 '12 at 22:42
    
I wouldn't insist on any rule since there are only conventions not rules, it's the message that is carried across. If you can safely transmit the message that it's the differential operator you are done. If you have all the variables upright then $sin(x)$ would be the correct one since you are making a distinction not complying to a rule. –  percusse Nov 4 '12 at 22:50
    
@queueoverflow dy is similar, they can both be defined ans mathematical objects such that writing dy/dx = dy/dz dz/dx makes a perfect sense. I would say: Care about the proper spacing and upshape/italics is then irrelevant ;) –  yo' Nov 4 '12 at 22:54

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