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Math Help - Need help with this derivative please

  1. #1
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    Need help with this derivative please

    The problem is differentiate (r^2)/(sqrt[r]+1)

    I ended up with (3/2)r^(3/2)+2r in the numerator and (sqrt[r]+1)^2 in the denominator.

    Is this correct so far and if so how do I simplify it more?

    The answer apparently is r(4+3sqrt[r]) in the numerator and 2(1+sqrt[r])^2 in the denominator.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by kep84 View Post
    The problem is differentiate (r^2)/(sqrt[r]+1)

    I ended up with (3/2)r^(3/2)+2r in the numerator and (sqrt[r]+1)^2 in the denominator.

    Is this correct so far and if so how do I simplify it more?

    The answer apparently is r(4+3sqrt[r]) in the numerator and 2(1+sqrt[r])^2 in the denominator.
    you mean \frac {d}{dr} \frac {r^2}{\sqrt {r} + 1} ?

    if so, you are correct. i wouldn't really worry about simplifying anymore. it's fine
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  3. #3
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    yay i'm right i figured that my answer was fine, but now i am curious to see how they got to that form.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by kep84 View Post
    yay i'm right i figured that my answer was fine, but now i am curious to see how they got to that form.
    what form did they get it to? maybe they used the product rule and not the quotient rule
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  5. #5
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    Quote Originally Posted by Jhevon View Post
    what form did they get it to? maybe they used the product rule and not the quotient rule

    Quote Originally Posted by kep84 View Post
    The answer apparently is r(4+3sqrt[r]) in the numerator and 2(1+sqrt[r])^2 in the denominator.
    this
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by kep84 View Post
    this
    using the product rule i get \frac {4r + 3r^{3/2}}{2(\sqrt {r} + 1)^2} = \frac {r(4 + 3 \sqrt {r})}{2(\sqrt {r} + 1)^2} as desired

    to use the product rule, you must realize that \frac {r^2}{\sqrt {r} + 1} = r^2 (\sqrt {r} + 1)^{-1}
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