# Homework Help: Find derivative using Quotient rule

1. Oct 5, 2008

### DollarBill

1. The problem statement, all variables and given/known data
Differentiate

f(x) = 6-5x-x2 / x2-1
-------
A) -5-5x / x2-1

B) 5 / (x+1)2

C) -5-5x / (x2-1)2

D) -5 / (x+1)2

E) -5+5x / x2-1

F) None of the above

3. The attempt at a solution
(x2)(-5-2x)-(6-5x-x2)(2x) / (x2-1)2

Simplified to:

5x2-10x+5 / x4-2x2+1

But it's not one of the answer choices. I tried simplifying it even further to:

5(x2-2x) / x4-2x2+1
or
5(x2-2x) / (x2-1)2

But I can't see where else to go with it.

2. Oct 5, 2008

### rocomath

Ok so you're taking a quiz or exam? So I think it's best to wait till you're done :)

3. Oct 5, 2008

### DollarBill

It actually is just homework

4. Oct 5, 2008

### rocomath

I don't see much hw with multiple choice, so yeah ...

5. Oct 5, 2008

### DollarBill

I don't even get the benefit of the doubt? I can guarantee you that this is just a homework problem.

But if you're not going to believe or help me, can you at least tell me if I'm headed in the right direction or did I miss something?

6. Oct 5, 2008

### JG89

"(x^2)(-5-2x)-(6-5x-x^2)(2x) / (x2-1)^2"

the first (x^2) should be (x^2 - 1)

it could also be possible that the answers you are given are in a simplified form. What are the answers?

7. Oct 5, 2008

### DollarBill

These are the choices:

(A) -5-5x / x2-1

(B) 5 / (x+1)2

(C) -5-5x / (x2-1)2

(D) -5 / (x+1)2

(E) -5+5x / x2-1

(F) None of the above

-------------

Yea, I forgot to put the "-1", but I did do it on my paper.

From:
(x2-1)(-5-2x)-(6-5x-x2)(2x) / (x2-1)2

I got:
-5x2+5-2x3+2x-12x+10x2+2x3 / x4-2x2+1

Simplified to:
5x2-10x+5 / x4-2x2+1

to

5(x2-2x+1) / (x2-1)2
or
5(x-1)2 / (x2-1)2

But I don't know where to go from there

8. Oct 5, 2008

### Skatch

5(x-1)2 / (x2-1)2 is correct thusfar. Just notice that (x2-1) is a difference of two squares. Change it to (x+1)(x-1) and your answer simplifies to (B), which should be correct.

Last edited: Oct 5, 2008
9. Oct 5, 2008

### DollarBill

I completely missed that. Thanks!