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

[vkash]

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[micromass]

It's the Leibniz notation for the derivative. See http://en.wikipedia.org/wiki/Derivative

 

[vkash]

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.

 

[micromass]

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.

 

[romsofia]

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, $${y=x^2}$$ 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 $${1*dy/dx=2x}$$

Hopefully my explanation is clear haha.

 

[dalcde]

It does, in some sense, mean $\mathrm dy$ divided by $\mathrm dx$ in nonstandard calculus, where we use infinitesimals instead of limits to do calculus.