Is d(2x) equal to dx in Calculus?

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The derivative of the function d(2x) is equal to 2dx, not dx, because the constant 2 must be accounted for in differentiation. This is established by the differentiation rule where the derivative of a constant multiplied by a variable is the constant itself. The discussion clarifies that while constants can be ignored when added to a function, they cannot be ignored when multiplied by a variable. Thus, the relationship between d(2x) and dx is directly proportional, with a factor of 2.

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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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JamesGoh said:
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?
 
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.
 
JamesGoh said:
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 =]
 
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.
 
JamesGoh said:
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:
 
thanks everyone ! you helped solved my problem
 

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