- #1
Jason Ko
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- What's the difference between d,d/dx and dx?
What's the difference between d,d/dx and dx?
What's the difference between d, d/dx and dx?
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- Thread starter Jason Ko
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The "top" of the fraction is the result of applying the operator ##\frac d{dx}## to the function f.In summary, the difference between d, d/dx, and dx is that d has no independent meaning in terms of calculus, d/dx denotes the derivative of a function with respect to x, and dx represents the differential of the variable x, which can be thought of as a small change in x. The operator d/dx applied to a function produces the derivative of the function with respect to x.
- #2
anuttarasammyak
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For an example of function ##y = \sin x##.
[tex]dy=\cos x \ \ dx[/tex]
dx is infinitesimal change of x and dy is change corresponding to dx.
[tex]\frac{d}{dx}\ y=\frac{dy}{dx}= \cos x[/tex]
##\frac{d}{dx}## is operator to make differential coefficient
which is expressed as the ratio ##\frac{dy}{dx}##.
[tex]dy=\cos x \ \ dx[/tex]
dx is infinitesimal change of x and dy is change corresponding to dx.
[tex]\frac{d}{dx}\ y=\frac{dy}{dx}= \cos x[/tex]
##\frac{d}{dx}## is operator to make differential coefficient
which is expressed as the ratio ##\frac{dy}{dx}##.
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- #3
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Jason Ko said:
##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
- #4
Mark44
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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.PeroK said:
If f is the function, then ##\frac {df}{dx}## is the derivative of f with respect to x.
Related to What's the difference between d, d/dx and dx?
1. What is the definition of d, d/dx, and dx?
The symbol "d" is used to represent the derivative operator, which indicates the rate of change of a function. "d/dx" is read as "the derivative with respect to x" and is used to denote the specific variable with respect to which the derivative is being taken. "dx" represents an infinitesimal change in the variable x.
2. What is the difference between d and d/dx?
The main difference between d and d/dx is that "d" is a general symbol for the derivative operator, while "d/dx" is more specific and indicates that the derivative is being taken with respect to the variable x. "d" can be used to take derivatives with respect to other variables, such as dy/dt, while "d/dx" is used specifically for derivatives with respect to x.
3. How do you read d/dx?
"d/dx" is read as "the derivative with respect to x." This means that we are finding the rate of change of a function with respect to the variable x.
4. What is the purpose of dx in calculus?
In calculus, dx represents an infinitesimal change in the variable x. It is used to indicate that we are taking the derivative with respect to x and helps us to understand the concept of instantaneous rate of change. It is also used in integrals to represent an infinitely small width of a rectangle under a curve.
5. Can d/dx and dx be used interchangeably?
No, d/dx and dx cannot be used interchangeably. "d/dx" is an operator that represents the derivative with respect to x, while dx represents an infinitesimal change in x. They are two separate symbols with different meanings and cannot be used interchangeably.
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