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Need help on find the derivitave

  1. Oct 27, 2011 #1
    1. The problem statement, all variables and given/known data

    So f(x)= x(√x-1)

    2. Relevant equations

    3. The attempt at a solution

    So i understand that the derivitive of a mutiple is (f x g) prime

    f'xg + fxg'

    I got

    (1)(√x-1) + (x)(1/2x^-1/2)

    now im stuck...

    ive used the equation (f(x)-f(x))/x-a and i ended up with x^3/2 -1

    but when i used (f')(g)+(f)(g)'

    i get 3/2x^1/2 - 1

    and now i am just really confused... i could really use some help :D
    Last edited: Oct 27, 2011
  2. jcsd
  3. Oct 27, 2011 #2


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    Homework Helper

    Is [itex]f(x) = x(\sqrt{x}-1)[/itex] or [itex]f(x) = x(\sqrt{x-1})[/itex]?

    Don't forget parentheses. I'm sure you mean (1)(√x-1) + (x)((1/2)x^-1/2).
  4. Oct 27, 2011 #3
    okay so f(x)= x((sqrtx) -1)

    the square root only applies to x. not 1

    okay so (1)(√x-1)= √x-1

    (x)(√x-1)' is essentially (x)(1/2x^-1/2) is it not?

    There for we have

    √x-1 + (x)(1/2x^-1/2)

    Now im not sure if im doing this right but

    (x)(1/2x^-1/2)= 1/2x^1/2

    Assuming i am right then we have

    √x-1 + 1/2x^1/2
    = (x^1/2 -1) + (1/2x^1/2)
    =3/2x^1/2 - 1

    Now is that it?
  5. Oct 28, 2011 #4


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    Homework Helper

    That looks fine.
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