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Very simple calculus question

  1. Apr 19, 2009 #1
    Just a very simple question in calculus, does d(2x) = dx because 2 is a constant, therefore we can just ignore the 2 ?
     
  2. jcsd
  3. Apr 19, 2009 #2

    Doc Al

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    Staff: Mentor

    No. d(2x) = 2dx.

    Consider y = ax, where a is a constant. What's dy/dx?
     
  4. Apr 21, 2009 #3
    I think that you may be thinking of when a constant is added to a function. That is when the constant may be ignored in differentiation.
     
  5. Apr 21, 2009 #4

    djeitnstine

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    Gold Member

    As the previous poster said d(2x) = 2dx. 'dx' is simply a differential, it is not an operator. I won't get any more technical on that, I'll leave that to the math gurus =]
     
  6. Apr 21, 2009 #5
    To see that d(2x) = 2dx, you can use the fact that you know:

    (d/dx)2x = 2

    Treating dx as an infinitesimal (as is done when talking about linear approximations to functions using differentials), you can get

    (d)2x = 2(dx).

    Treating derivatives like fractions, as was just done, usually works, but you have to be careful.
     
  7. Apr 21, 2009 #6
    No, they are related directly proportionally by a factor of 2.

    .....

    Sorry, I just wanted to get in on that action of saying the same thing in different ways. :smile:
     
  8. Apr 22, 2009 #7
    thanks everyone ! you helped solved my problem
     
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