Very simple calculus question

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Just a very simple question in calculus, does d(2x) = dx because 2 is a constant, therefore we can just ignore the 2 ?
 

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  • #2
Doc Al
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Just a very simple question in calculus, does d(2x) = dx because 2 is a constant, therefore we can just ignore the 2 ?
No. d(2x) = 2dx.

Consider y = ax, where a is a constant. What's dy/dx?
 
  • #3
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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.
 
  • #4
djeitnstine
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Just a very simple question in calculus, does d(2x) = dx because 2 is a constant, therefore we can just ignore the 2 ?
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 =]
 
  • #5
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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.
 
  • #6
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Just a very simple question in calculus, does d(2x) = dx because 2 is a constant, therefore we can just ignore the 2 ?
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:
 
  • #7
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thanks everyone ! you helped solved my problem
 

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