- #1
JamesGoh
- 140
- 0
Just a very simple question in calculus, does d(2x) = dx because 2 is a constant, therefore we can just ignore the 2 ?
Is d(2x) equal to dx in Calculus?
- Context: High School
- Thread starter JamesGoh
- Start date
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- Calculus
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Discussion Overview
The discussion revolves around the differentiation of the expression d(2x) in calculus, specifically whether it is equal to dx or not. The scope includes conceptual clarification and mathematical reasoning related to differentiation rules.
Discussion Character
- Conceptual clarification, Mathematical reasoning, Debate/contested
Main Points Raised
- Some participants propose that d(2x) could equal dx because 2 is a constant and may be ignored in differentiation.
- Others argue that d(2x) actually equals 2dx, emphasizing that the constant affects the differential.
- A participant suggests that the confusion may stem from the differentiation of constants added to functions, where the constant can be ignored.
- Another participant clarifies that dx is a differential and not an operator, reinforcing that d(2x) = 2dx.
- One participant illustrates the reasoning by referencing the derivative of 2x, stating that (d/dx)2x = 2, and connects this to the treatment of differentials as infinitesimals.
- A later reply humorously acknowledges the repetition of the same point in various ways, indicating a light-hearted engagement with the topic.
Areas of Agreement / Disagreement
Participants generally disagree on whether d(2x) can be simplified to dx, with multiple competing views on the relationship between d(2x) and dx remaining unresolved.
Contextual Notes
Some limitations include the potential misunderstanding of the role of constants in differentiation and the treatment of differentials as infinitesimals, which may not be universally accepted or understood.
- #2
Doc Al
Mentor
- 45,581
- 2,455
No. d(2x) = 2dx.JamesGoh said:
Consider y = ax, where a is a constant. What's dy/dx?
- #3
22/7
- 7
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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
Gold Member
- 611
- 0
JamesGoh said:
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
AUMathTutor
- 498
- 0
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.
(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
elect_eng
- 372
- 2
JamesGoh said:
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.
- #7
JamesGoh
- 140
- 0
thanks everyone ! you helped solved my problem
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