What is the Meaning of dy/dx in Nonstandard Calculus?

  • Thread starter vkash
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In summary, the Leibniz notation, or dy/dx, is a notation for the derivative with respect to y. It is equivalent to f'(x) and represents taking the derivative of y with respect to x. In some nonstandard calculus methods, it can be interpreted as dy divided by dx.
  • #1
vkash
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  • #3
micromass said:
It's the Leibniz notation for the derivative. See http://en.wikipedia.org/wiki/Derivative
very long article.
Actually the thing i want to ask is Does dy/dx means dy divided by dx.
 
  • #4
vkash said:
very long article.
Actually the thing i want to ask is Does dy/dx means dy divided by dx.


Not at all! dy/dx is simply a notation. It's a notation for the derivative with respect to y.
 
  • #5
It means the same thing as f'(x) does. Take whatever y is and take the derivative of it with respect to x.
If we have the equation, [tex]{y=x^2}[/tex] what's the derivative with respect to x? We have to use implicit differentiation because you can't the derivative of y when we are taking it it with respect to x. So you have [tex]{1*dy/dx=2x}[/tex]

Hopefully my explanation is clear haha.
 
  • #6
It does, in some sense, mean [itex]\mathrm dy[/itex] divided by [itex]\mathrm dx[/itex] in nonstandard calculus, where we use infinitesimals instead of limits to do calculus.
 

1. What does dy/dx represent?

Dy/dx represents the derivative of a function, which is the rate of change of the function at a specific point.

2. What is the difference between dy/dx and y?

Dy/dx represents the instantaneous rate of change of a function, while y represents the value of the function at a specific point.

3. How do you find the value of dy/dx?

To find the value of dy/dx, you can use the derivative rules such as the power rule, product rule, quotient rule, or chain rule, depending on the type of function given.

4. Why is dy/dx important in calculus?

Dy/dx is important in calculus because it allows us to analyze the behavior of functions and solve problems involving rates of change, optimization, and motion.

5. Can dy/dx be negative?

Yes, dy/dx can be negative. The sign of dy/dx depends on the direction of change of the function at a specific point. A negative value of dy/dx indicates a decreasing function, while a positive value indicates an increasing function.

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