# find the derivative

• Jul 28th 2010, 05:24 PM
superduper1
find the derivative
$y=(\frac{x^2+1}{x^2-1})^3$

I used quotient rule and chain rule.
The solution keep getting is wrong. I think my algebra is off.: $y'= \frac{12x(x^2+1)^2}{(x^2-1)^4}$
• Jul 28th 2010, 05:29 PM
Also sprach Zarathustra
y'=3{(x^2+1)/(x^2-1)}^2 * {2x(x^2-1)-2x(x^2+1)}/{x^2-1}^2=...
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=3{(x^2+1)/(x^2-1)}^2 * {2x{x^2-1-x^2-1}/{(x^2-1)^2}=

=3{(x^2+1)/(x^2-1)}^2 * {2x{-2}/{(x^2-1)^2}=

=3{(x^2+1)/(x^2-1)}^2 * {-4x/{(x^2-1)^2}=

=-12x/(x^2-1)}^4
• Jul 28th 2010, 05:30 PM
skeeter
Quote:

Originally Posted by superduper1
$y=(\frac{x^2+1}{x^2-1})^3$

I used quotient rule and chain rule.
The solution keep getting is wrong. I think my algebra is off.: $y'= \frac{12x(x^2+1)^2}{(x^2-1)^4}$

show your work so that someone may see your mistake.
• Jul 28th 2010, 05:31 PM
pickslides
I get $y = \frac{6x(x^2-1)^3(x^2+1)^2-6x(x^2-1)^2(x^2-1)^3}{(x^2-1)^6}$

take out common factors to do some additional cancellations.
• Jul 28th 2010, 05:42 PM
superduper1
I think the mistake is somewhere after here:

$y'=3(\frac{x^2+1}{x^2-1})^2 * \frac{2x[x^2+1-x^2+1]}{(x^2-1)^2}$
$y'=3(\frac{x^2+1}{x^2-1})^2 * \frac{2x(2)}{(x^2+1)^2}$

What is this when simplified? I think this is throwing me off. The 3 in front and the ^2 in the back
$y'=3(\frac{x^2+1}{x^2-1})^2$
• Jul 28th 2010, 06:51 PM
skeeter
$\displaystyle y=\left(\frac{x^2+1}{x^2-1}\right)^3$

$\displaystyle \frac{dy}{dx} = 3\left(\frac{x^2+1}{x^2-1}\right)^2 \cdot \frac{(x^2-1)(2x) - (x^2+1)(2x)}{(x^2-1)^2}$

$\displaystyle \frac{dy}{dx} = 3\left(\frac{x^2+1}{x^2-1}\right)^2 \cdot \frac{2x[x^2-1 - (x^2+1)]}{(x^2-1)^2}$

$\displaystyle \frac{dy}{dx} = 3\left(\frac{x^2+1}{x^2-1}\right)^2 \cdot \frac{-4x}{(x^2-1)^2}$