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Math Help - finding the error in differentiation

  1. #1
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    finding the error in differentiation

    Hello all,
    This is a differentiaiton question given to me by my friend.I could not find the mistake in the proof.
    x = x
    x = 1 + 1 + ... + 1 (x times)
    multiplying by x
    x(x) = x(1 + 1 + ... + 1)
    x2 = x + x + ... + x
    D(x2) = D(x + x + ... + x)
    D(x2) = D(x) + D(x) + ... + D(x)
    2x = 1 + 1 + ... + 1 (x times)
    2x = x
    2 = 1

    i think it is somewhere in the differentiation .But couldnot get it.

    i hope i have not made a mistake by posting in the wrong forum.
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  2. #2
    Moo
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    Hello,

    x = 1 + 1 + ... + 1 (x times)
    You cannot write it unless x is a positive integer.
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  3. #3
    MHF Contributor

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    Also in "x= 1+ 1+ ...+ 1 (x times)" or " x^2= x+ x+ x+ ...+ x (x times)" the number of terms in the sum is itself a function of x and the differentiation rule (f+ g)'= f'+ g' does not apply.
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