# Homework Help: Quotient rule Differentiation

1. Jan 19, 2012

### Nitrate

1. The problem statement, all variables and given/known data
a) Differentiate y=((x-1)/(x+1))^2

b (non calculus simplification question):
How would i simplify 10(5x+3)(5x-1)+5(5x-1)^2 to get 25(5x-1)(3x+1)
should i expand all terms then combine and factor?

2. Relevant equations

3. The attempt at a solution
a) i tried using the quotient rule but kept ending up with missing terms...
from the answer key i know that the answer is (4(x-1))/(x+1)^3
but i can't get that for the life of me...

2. Jan 19, 2012

### iRaid

Re: Differentiation

Chain rule on this simplifies it a lot.. (if you know it?)

$y=u^{2}$

$u=\frac{x-1}{x+1}$

EDIT: Just in case you don't knnow, take the derivative of y and u then do the following:

$\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}$

Last edited: Jan 19, 2012
3. Jan 19, 2012

### Nitrate

Re: Differentiation

i do
however i've never really learned it using substitutions.
would i bring up the (x+1)^2 to the top, so that the equation becomes (x-1)^2(x+1)^-2?
or would that further complicate things

4. Jan 19, 2012

### iRaid

Re: Differentiation

I editted my post, maybe that will help you