# Quotient Rule - Can't get correct answer

• Aug 9th 2009, 07:35 AM
Macca567
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 :/.
• Aug 9th 2009, 07:57 AM
Plato
$\displaystyle \begin{gathered} y = \frac{x} {{\sqrt {x + 1} }} = x\left( {x + 1} \right)^{-\frac{{ 1}} {2}} \, \hfill \\ \Rightarrow \,y' = \left( {x + 1} \right)^{-\frac{{ 1}} {2}} + \frac{{ - x}} {2}\left( {x + 1} \right)^{-\frac{{ 3}} {2}} \hfill \\ \end{gathered}$
• Aug 9th 2009, 08:35 AM
skeeter
Quote:

Originally Posted by Macca567
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 :/.

$\displaystyle \frac{d}{dx} \left(\frac{x}{\sqrt{x+1}}\right)$

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

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

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

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