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    (I do A2, if I've made a glaring mistake here like I believe I have please point it out)

    Now as I'm sure everyone is aware, any number other than zero divided by zero has no value, however something odd happens when I differentiate the function


    y=x/0


    U=x V=0


    y=U/V


    Quotient rule


    dy/dx=(V(du/dx)-U(dv/dx))/V^2


    Substitute x and zero back in


    dy/dx=(0-0)/0


    Here's the weird part, 0/0 can be anything, so for any value of x, even though y is undefined, dy/dx is equal to every single number at the same time... How very... odd...

    I await patronising explanations of some fundamental misunderstanding

    Edit: The obvious absurdity here

    dy/dx=0/0

    y=Integral 0/0 dx

    (Multiplying anything by zero is zero so I can shove in an x I think)

    y= integral 0/0x dx

    y=ln0x=ln0 (I don't think I can do that)

    x/0(Is identical to)ln0

    0/0=ln0

    ln0 is defined as all numbers

    x/0 satisfies all values
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    Dividing by zero glitches maths. If you allow dividing by zero, pi = 42 and 3=eleventy twelve.

    Hence the odd results.

    (Disclaimer: I'm only an A2 student, hence the simplistic reply. I await some postgrad to use axiomatic set theory to prove why this happens)

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    Before I'm slam dunked can I suggest that it's probably because the proof of the quotient rule assumes you are not trying to divide by zero?
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    If maths is inconsistent then absolutely everything is true. Since x/0 being well defined would make maths inconsistent, you can use it to prove absolutely anything.
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    A function has to be continuous to be differentiable at a point ergo you cannot differentiate x/0 as its not a continuous function.
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    (Original post by MM04926412)
    Before I'm slam dunked can I suggest that it's probably because the proof of the quotient rule assumes you are not trying to divide by zero?
    Try using product rule. Ie x(0)^-1 ha.


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    (Original post by Mathlover123)
    A function has to be continuous to be differentiable at a point ergo you cannot differentiate x/0 as its not a continuous function.
    It isn't even a function.
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    (Original post by physicsmaths)
    Try using product rule. Ie x(0)^-1 ha.


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    You realise that the quotient rule is just the product rule?
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    (Original post by TenOfThem)
    You realise that the quotient rule is just the product rule?
    obviously as thats why i rewrote his thing so he could use the product rule


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    (Original post by TenOfThem)
    You realise that the quotient rule is just the product rule?
    y=uv^-1 and differentiating gives quotient rule.
    i wrote ha at then end for a reason lol.


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    (Original post by physicsmaths)
    obviously as thats why i rewrote his thing so he could use the product rule


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    (Original post by physicsmaths)
    y=uv^-1 and differentiating gives quotient rule.
    i wrote ha at then end for a reason lol.


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    I guess you were trying to make a point that I have failed to grasp
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    (Original post by TenOfThem)
    I guess you were trying to make a point that I have failed to grasp
    Lol no i was joking and wanted tos ee if he would realise what u said. thats why i wrote ha at the end lol.


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    (Original post by james22)
    It isn't even a function.
    Yeah I guess that's just as fair a point to differentiate a function you must at least have a function.
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    (Original post by physicsmaths)
    Lol no i was joking and wanted tos ee if he would realise what u said. thats why i wrote ha at the end lol.
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