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Math Help - Finishing this derivative problem (work included)

  1. #1
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    Exclamation Finishing this derivative problem (work included)

    Can someone please help me finish this derivative problem?
    Here's the problem:

    f(v) = [ (1-2v) / (1+v) ] ^ 3

    Here's my work so far:

    f '(v) = 3[ (1-2v) / (1+v)] ^2 times [(1+v)(-2) - (1-2v)(v) / (1+v)^2 ]
    f '(v) = [3(1-2v)^2] / (1+v)2 times [-2 - 2v - v + 2v^2] / (1+v)^2 ]
    f '(v) = " times (-2-3v+2v^2) / (1+v)^2
    f '(v) = [3(1-2v)^2][-2-3v+2v^2] / [1+v]^4


    ..thats as far as I got, but the answer is: [ -9(2v - 1)^2 ] / (1+v)^4

    How did they get that??
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by janedoe View Post
    [snip]

    Here's my work so far:

    f '(v) = 3[ (1-2v) / (1+v)] ^2 times [(1+v)(-2) - (1-2v)(1) / (1+v)^2 ]

    [/snip]
    See my minor correction in red.
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  3. #3
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    Ahh thank you!!

    But now I get: -9(1-2v)^2 / (1+v)^4

    their answer is 2v-1 instead ... ?
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  4. #4
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    is the answer: 3*[(1-2v)^2*(v-3)]/[1+v)^4
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  5. #5
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    no its



    but I keep getting 1-2v in stead of 2v-1 and so does my friend....so we think it's the book's error.
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  6. #6
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    this is my solution

    = [(1-2v)/(1+v)]^3
    = 3*[[(1-2v)/(1+v)]^2]*[(1-2v+2+2v)/[(1+v)^2]]
    = 9*[[(1-2v)^2]/[(1+v)^4]]
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  7. #7
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    Man, don't you know that
    (a-b)^2=(b-a)^2 .It's really easy to prove this.
    So (1-2v)^2=(2v-1)^2 and your's and book's answer is correct.
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  8. #8
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    Hello, janedoe!

    But now I get: . \frac{-9(1-2v)^2}{(1+v)^4}

    Their answer has (2v-1)^2
    You both are correct!

    Note that: . (1-2v)^2 \:=\: (2v-1)^2


    But I have no idea why they switched that binomial.
    .
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  9. #9
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    I don't think there's a - sign, my answer is 9, not -9
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