Find derivative using Quotient rule

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Homework Help Overview

The discussion revolves around differentiating the function f(x) = (6 - 5x - x²) / (x² - 1) using the Quotient Rule. Participants are exploring the differentiation process and comparing their results to multiple-choice answer options.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to differentiate the function using the Quotient Rule and simplifies their result, but finds it does not match any of the provided answer choices. Other participants question the correctness of the differentiation steps and suggest possible simplifications.

Discussion Status

Participants are actively discussing the differentiation process, with some offering guidance on potential simplifications and corrections to the original poster's approach. There is no explicit consensus on the final answer, but a productive direction is noted as one participant identifies a simplification that aligns with one of the answer choices.

Contextual Notes

There is a mention of the problem being part of a homework assignment, and some participants express skepticism about the nature of the problem due to its multiple-choice format. The original poster clarifies that it is indeed homework, which influences the tone of the discussion.

DollarBill
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Homework Statement


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

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.
 
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Ok so you're taking a quiz or exam? So I think it's best to wait till you're done :)
 
It actually is just homework
 
I don't see much homework with multiple choice, so yeah ...
 
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?
 
"(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?
 
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
 
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:
I completely missed that. Thanks!
 

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