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Math Help - Quotient Rule - Can't get correct answer

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    Quotient Rule - Can't get correct answer

    Hey, Got a Maths exam tomorrow and I'm having a bit of trouble trying to get the answer given in the back of the book for this problem:

    I have to differentiate this:

    x/(x+1)^1/2 The answer in the back is x+2/2(x+1)^3/2

    I get to: (((x+1)^-1/2) -1/2x.((x+1)^-3/2))/(x+1)

    But I can't make the jump from this line to the answer :/.
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    \begin{gathered}<br />
  y = \frac{x}<br />
{{\sqrt {x + 1} }} = x\left( {x + 1} \right)^{-\frac{{  1}}<br />
{2}} \, \hfill \\<br />
   \Rightarrow \,y' = \left( {x + 1} \right)^{-\frac{{  1}}<br />
{2}}  + \frac{{ - x}}<br />
{2}\left( {x + 1} \right)^{-\frac{{  3}}<br />
{2}}  \hfill \\ <br />
\end{gathered}
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  3. #3
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    Quote Originally Posted by Macca567 View Post
    Hey, Got a Maths exam tomorrow and I'm having a bit of trouble trying to get the answer given in the back of the book for this problem:

    I have to differentiate this:

    x/(x+1)^1/2 The answer in the back is x+2/2(x+1)^3/2

    I get to: (((x+1)^-1/2) -1/2x.((x+1)^-3/2))/(x+1)

    But I can't make the jump from this line to the answer :/.
    \frac{d}{dx} \left(\frac{x}{\sqrt{x+1}}\right)

    \frac{\sqrt{x+1} \cdot 1 - x \cdot \frac{1}{2\sqrt{x+1}}}{x+1}

    multiply by \frac{2\sqrt{x+1}}{2\sqrt{x+1}} ...

    \frac{2(x+1) - x}{2(x+1)^{\frac{3}{2}}}

    \frac{x+2}{2(x+1)^{\frac{3}{2}}}
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