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Math Help - Given function and given differential of the function - how do I get there?

  1. #1
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    Given function and given differential of the function - how do I get there?

    Hey mathematicians,

    I have looked at this for quite some time...

    I have (which is given)

    f(x) = 2*x^2 / (x^4 +1)

    and I have (which is also given)

    f ' (x) = ( 4x (1 + x^2) (1+x) (1-x) ) / (x^4 + 1)^2

    ... So, I'm looking to find the steps to get to the given f ' (x)...

    I have already worked quite a lot on it, but what i end getting is this...

    I won't get into the (x^4 + 1)^2-part - as it is quite simple, but I get...

    - 4x^5 + 4x => -4x (x^4 - 1)

    Okay, so how do I get the last expression into factors?

    What bothers me is the minus in front of 4x..? How do I get rid of it?


    I hope someone has the time to help me out... It would be much appreciated.

    Yours sincerely, Simon, DK.
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  2. #2
    Grand Panjandrum
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    -4x (x^4 - 1) = -4x (x^2-1)(x^2+1) - using difference of two squares x^4 and 1

    -4x (x^4 - 1) = -4x (x-1)(x+1)(x^2+1) - difference of two squares again x^2 and 1 in this case

    -4x (x^4 - 1) = 4x (1-x)(x+1)(x^2+1) - using -(x-1)=(1-x).

    RonL
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  3. #3
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    Hello, Simon!

    -4x^5 + 4x \;= \;-4x(x^4 - 1)

    What bothers me is the minus in front of 4x . . . How do I get rid of it?

    Multiply through by it:

    . . -4x(x^4-1) \;=\;4x(-x^4 + 1) \;=\;4x(1 - x^4)

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  4. #4
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    Thank you!

    Thank you very much. Quick reply. Perfect.
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