B What's the difference between d, d/dx and dx?

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What's the difference between d,d/dx and dx?
What's the difference between d,d/dx and dx?
 
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For an example of function ##y = \sin x##.
dy=\cos x \ \ dx
dx is infinitesimal change of x and dy is change corresponding to dx.
\frac{d}{dx}\ y=\frac{dy}{dx}= \cos x
##\frac{d}{dx}## is operator to make differential coefficient
which is expressed as the ratio ##\frac{dy}{dx}##.
 
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Jason Ko said:
Summary:: What's the difference between d,d/dx and dx?

What's the difference between d,d/dx and dx?
:welcome:

##d## has no independent meaning in terms of calculus.

##d/dx## denotes the derivative (of a function) with respect to ##x##.

##dx## denotes the differential of the variable ##x##. Informally, you can think about it as a very small or infinitesimal change in ##x##. More formally, it is as described in post #2 above and here, for example:

https://tutorial.math.lamar.edu/classes/calci/differentials.aspx
 
PeroK said:
d/dx denotes the derivative (of a function) with respect to x.
Your explanation doesn't distinguish between the action of taking a derivative, versus the derivative itself. I would say that ##\frac d{dx}## is the operator that when applied to a function, produces the derivative of the function with respect to x.
If f is the function, then ##\frac {df}{dx}## is the derivative of f with respect to x.
 

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