1. Joined
    29 Feb '04
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    22
    06 Jun '04 09:40
    d(x^2)/dx = x

    PROOF:

    d(x^2)/dx = d(x + x + x + ....... (x times))/dx

    = d[x]/dx + d[x]/dx + d[x]/dx....... (x times)

    = 1 + 1 + 1 + ....... (x times)

    = x

    QED

    😉
  2. Standard memberTheMaster37
    Kupikupopo!
    Out of my mind
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    20443
    06 Jun '04 16:511 edit
    Now for integer (non-positive), rational (non-integer) or real (non-rational) x
  3. Joined
    29 Feb '04
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    22
    07 Jun '04 06:111 edit
    Originally posted by TheMaster37
    Now for integer (non-positive), rational (non-integer) or real (non-rational) x
    I guess 'Now...' should be "Not...'

    But hey, I'm not greedy - if it holds for the positive integers, that's OK by me. 😏

    .
  4. Standard memberTheMaster37
    Kupikupopo!
    Out of my mind
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    07 Jun '04 17:58
    😉

    I could point out that d/dx is defined with limits, the quotient of the horizontal and vertical displaccement in a graph, with the horizontal displacement going to 0. Since that limit process is kinda abrubt on the integers; 3,2,1,0,0,0,0... you divide by 0 and can get any answer you like.

    Assuming the limit process is correctly defined for natural numbers...
  5. DonationAcolyte
    Now With Added BA
    Loughborough
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    07 Jun '04 19:07
    How about this: let f(x) = x*[x], where [x] is the integer of smallest modulus which has greater modulus than x.

    If x isn't an integer, f'(x) = [x]
    OTOH if g(x) = x^2, g'(x) = 2x

    So on the set of positive reals which aren't integers, f and g are differentiable and g' - f' tends to infinity as x tends to infinity, but f > g for all x. (*)

    This is a demonstration of why your domain must be connected if you want differentiable (and indeed continuous) functions to behave themselves. For example, it's not possible to find two functions which satisfy (*) on all the positive reals.
  6. Standard memberTheMaster37
    Kupikupopo!
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    07 Jun '04 20:22
    I'm a litle bit in the dark on what you mean by modulus...[x] is usually the entier-function; [x] is the greatest integer no exceeding x (a sort of rounding down).
  7. Joined
    27 May '04
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    2291
    09 Jun '04 13:27
    Originally posted by THUDandBLUNDER
    d(x^2)/dx = x

    PROOF:

    d(x^2)/dx = d(x + x + x + ....... (x times))/dx

    = d[x]/dx + d[x]/dx + d[x]/dx....... (x times)

    = 1 + 1 + 1 + ....... (x times)

    = x

    QED

    😉
    Brillient
  8. Joined
    27 May '04
    Moves
    2291
    09 Jun '04 13:28
    Originally posted by crec2k
    Brillient
    That was a purposeful mistake.
    FYI, myles is fat.
  9. Joined
    19 May '04
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    155
    09 Jun '04 13:29
    Originally posted by crec2k
    That was a purposeful mistake.
    FYI, myles is fat.
    It is true, i am very fat.😛
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