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I have a differential problem

$$d(-axdy)=-adxdy$$

$$d(-axdy)=-adxy$$

Which one is correct?

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Is it $d(-ax)dy=-adxdy$, any chance? –  Tapu Sep 2 '12 at 7:57
    
@Tapu what!? what you means –  albert2 Sep 2 '12 at 7:59
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Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. Titles should be informative. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. –  Jayesh Badwaik Sep 2 '12 at 9:09
    
For $d$ maybe they intend: use the product rule. $a$ is a constant, so the termm with $d(-a)$ is zero; also $d^2=0$, so the term with $d(dy)$ is zero. That leaves just one of the three terms: $-a dx dy$ . –  GEdgar Sep 2 '12 at 13:16
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closed as not a real question by Gigili, Matt N., Did, fpqc, wentaway Sep 2 '12 at 17:10

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1 Answer

If $z=f(x,y)$ then $dz=z_xdx+z_ydy$ provided $z$ has continuous first partial derivatives in a region.

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Good to help out the OP! +1 $\quad \ddot\smile \quad$ –  amWhy Mar 14 '13 at 2:05
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