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Thread: differentiable functions

  1. #1
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    differentiable functions




    can some kind soul tell me what is this question asking and how to solve it?
    Last edited by alexandrabel90; Jan 10th 2010 at 07:39 AM. Reason: couldnt see the image
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    The product rule for two functions is given by

    $\displaystyle (f \cdot g)' = f' \cdot g + f \cdot g\ $

    Using induction, prove that for any $\displaystyle n\geq2 $ number of functions, the generalized product rule (given to you) holds.

    Start with your base case. Assume. Work up.
    Last edited by abender; Jan 10th 2010 at 08:00 AM. Reason: latex poop
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  3. #3
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    may i know what does the LHS N look a like symbol from k=1 to n mean? this is the first time im seeing that symbol thats why.
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    $\displaystyle \mathbf{Z}^{+} $ represents the set of positive integers. 1, 2, 3, ...


    $\displaystyle \mathbf{R} $ represents the set of real numbers.
    1, 905, -763, 0.13244, 0, 2/5, anything that is real (read: not imaginary; no i)

    $\displaystyle \sum $ represents "the sum of." So, $\displaystyle \sum_{k=1}^n x^k = x^1 + x^2 + x^3 + ... + x^n $


    $\displaystyle \prod $ represents "the product of." So, $\displaystyle \prod_{k=1}^n x^k = x^1 \cdot x^2 \cdot x^3 \cdot ... \cdot x^n $
    Last edited by abender; Jan 10th 2010 at 10:05 AM. Reason: R....not R+
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    this is how i have done it..but i got stuck as to how to continue from there..
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  6. #6
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    Quote Originally Posted by abender View Post
    $\displaystyle \mathbf{Z}^{+} $ represents the set of positive integers. 1, 2, 3, ...


    ?$\displaystyle \mathbf{R}^{+} $? represents the set of real numbers.
    1, 905, -763, 0.13244, 0, 2/5, anything that is real (read: not imaginary; no i)

    $\displaystyle \sum $ represents "the sum of." So, $\displaystyle \sum_{k=1}^n x^k = x^1 + x^2 + x^3 + ... + x^n $


    $\displaystyle \prod $ represents "the product of." So, $\displaystyle \prod_{k=1}^n x^k = x^1 \cdot x^2 \cdot x^3 \cdot ... \cdot x^n $
    .
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  7. #7
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    how do you show that A(n+1) = 0 from my working and hence the equation is true by induction?
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    Quote Originally Posted by VonNemo19 View Post
    .
    oops, i was copy-pasting from the latex code above obviously...
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