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For example when integrating by substitution one would write dx=2u.du. In this what does the dx mean and why do we get it in equations like the above? What i am basically asking is why does x=u^2 mean that dx=2u.du where do the du and dx come from??

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    http://math.stackexchange.com/questions/143222/what-does-dx-mean?rq=1 – Alex Apr 08 '14 at 09:28
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    Until you get to higher calculus where such things are justified, I think that things like $\frac{du}{dx}=2x\implies dx=2xdu$ are, to put it uncharitably, meaningless gibberish. I'm just a student, but I have yet to see a single rigorous justification for manipulations like that. It does work, so presumably there is a justification, but personally I choose to see it as invalid, and prefer to write everything out in terms of functions and derivatives. – Jack M Apr 08 '14 at 09:55
  • I just found this webpage it has some useful info http://mathforum.org/library/drmath/view/65462.html –  Apr 08 '14 at 10:07
  • See also this: http://math.stackexchange.com/questions/665438/validity-of-substitutions-in-integrals – Hans Lundmark Apr 08 '14 at 10:07

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http://en.wikipedia.org/wiki/Derivative it is basically notation to represent derivative wrt to x.

aurilio
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