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Thread: Derivative

  1. #1 Derivative 
    Forum Masters Degree thyristor's Avatar
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    Considering to two main notations of derivative, is any of them 'better' than the other? My personal favourite is Lagrange's notation, but I have often heard that Leibniz' notation is more 'correct'. Have you got any comments on this?


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  3. #2  
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    What is Lagrange's notation for the derivative? As far as I am aware, the 2 in most common use are those of Newton and Leibniz.

    That said, notation is arbitrary, and, so as long as it is understood by all interlocutors, none is better than any other,


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  4. #3  
    Forum Masters Degree thyristor's Avatar
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    Lagrange's notation is f'(x).
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    Oops, yes, it appears you are right. Sorry
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    It depends on the context for me. I like Leibniz notation more as it seems to better portray the definition of the derivative. However, if I were looking at some type of differential equation like y''' + 3y'' - 2y' + y = 0 (off the top of my head), I would rather write it that way then in Leibniz notation.
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    I think the best notation depends a bit on what the context is. Like, if you've already said you have a function and call it f(x), then it's appropriate to use Lagrange's notation. But if you're just generally talking about the derivative of sine but haven't called it a function really, then you can just say .
    "There is a kind of lazy pleasure in useless and out-of-the-way erudition." -Jorge Luis Borges
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    Forum Masters Degree organic god's Avatar
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    I think as long as the notation is consistent it doesn't really matter, chaning between dy/dx and y' and f'(x) would be annoying to read
    everything is mathematical.
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  9. #8  
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    Quote Originally Posted by Guitarist
    What is Lagrange's notation for the derivative? As far as I am aware, the 2 in most common use are those of Newton and Leibniz.

    That said, notation is arbitrary, and, so as long as it is understood by all interlocutors, none is better than any other,
    Don't forget the dot

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    That's great, this forum page have a nice discussion.
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  11. #10  
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    does the dot only apply if it is the derivative with respect to time?
    everything is mathematical.
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  12. #11  
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    Quote Originally Posted by organic god
    does the dot only apply if it is the derivative with respect to time?
    Not necessarily, but it is most often used in that context.
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  13. #12 Re: Derivative 
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    Quote Originally Posted by thyristor
    Considering to two main notations of derivative, is any of them 'better' than the other? My personal favourite is Lagrange's notation, but I have often heard that Leibniz' notation is more 'correct'. Have you got any comments on this?
    It depends, but it can have some notable effects. Newton's notation dominated in Britain, and as a result of limiting themselves to Newton's methods instead of, for example, considering those of the likes of Bernoulli and others fell behind in calculus for over a century.

    Mathematics will enter new stages at various points in history, and countries must than keep up with them in order to keep up with various civilizations. The Babylonians had many of their concepts in Euclidean geometry and algebra borrowed by others such as the ancient Greeks. Britain's failure to do so obviously hurt them in terms of productive output and technological gain. The indefinite integral that Leibniz notated is considered inferior to the Riemann integral, which allows for calculating the area under a curve within an interval.
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    dy/dx!!!! woot
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