Find derivative of y= (x)/(x+y)

I used the quotient rule and then got y' on one side. My final answer is:

[(x+y)² - y] / (-2)

Is that correct?

Thanks!

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- Apr 27th 2009, 01:35 PMjanedoeIs my answer for derivative right
Find derivative of y= (x)/(x+y)

I used the quotient rule and then got y' on one side. My final answer is:

[(x+y)² - y] / (-2)

Is that correct?

Thanks! - Apr 27th 2009, 01:45 PMderfleurer
$\displaystyle y = \frac {x}{x + y}$

$\displaystyle y(x + y) - x = 0$

$\displaystyle xy + y^2 - x = 0$

$\displaystyle \frac {dy}{dx} = \frac {1 - y}{x + 2y}$ - Apr 27th 2009, 02:13 PMjanedoe
- Apr 27th 2009, 02:25 PMJameson
The answer that he/she gave looks correct to me. Please show your work for using the quotient rule and I'll try to spot an error if there is one.

- Apr 27th 2009, 02:31 PMjanedoe
- Apr 27th 2009, 02:45 PMJameson
Your work looks fine to me. I have a feeling that both answers are equivalent, but the algebra to change your form to the other is kind of messy. Maybe someone else can show that they are equal.

- Apr 27th 2009, 03:04 PMderfleurer
Looks right. Same thing I got using quotient rule. Wouldn't dare delve into the math to simplify them.