Derivative of x*sqrt[x/(2-x)] - Solving for the Correct Answer

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Homework Help Overview

The discussion revolves around finding the derivative of the function x*sqrt[x/(2-x)]. Participants are exploring various approaches to differentiate this expression, which involves multiple rules of calculus.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants present different derivative results and question the correctness of each other's answers. There is mention of applying the product rule, chain rule, and quotient rule in the differentiation process. Some participants express uncertainty about the classification of the problem as a "simple derivative."

Discussion Status

Multiple interpretations of the derivative have been shared, with some participants suggesting that one answer may be more accurate than another. There is no explicit consensus, but some guidance on the differentiation process has been provided.

Contextual Notes

One participant notes being away from math for a long time, indicating a potential challenge in recalling differentiation techniques. The thread has been active for several months, suggesting ongoing interest in the problem.

hanelliot
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Homework Statement


derivative of x*sqrt[x/(2-x)]


Homework Equations





The Attempt at a Solution


my friend got 1/(2-x) and I got {-(x-3)*[-x/(x-2)]^3/2}/x. Who's right?
 
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If I'm reading your problem correct, your answer seems more correct than his.

I've got [(sqrt x)*(3-x)]/[(2-x)^(3/2)] which should be the same answer in a more simplified format.

Now my question is: what kind of class are you taking where you would call this a "simple derivative"? :)
 
I don't think either of you is correct, and your friend is very far off. Your answer doesn't appear to be correct, but at least I can see how you are thinking. To do this problem you will have to apply, in this order,
  1. the product rule,
  2. the chain rule,
  3. the quotient rule
 
mrkuo said:
If I'm reading your problem correct, your answer seems more correct than his.

I've got [(sqrt x)*(3-x)]/[(2-x)^(3/2)] which should be the same answer in a more simplified format.

Now my question is: what kind of class are you taking where you would call this a "simple derivative"? :)
multivariable calculus II, I've been away from math for a long time and this is embarrassing.. anyways, ur answer = mine (plugged in few numbers to confirm), thanks all!
 
I got 1/[(2-x)^2]
 
lmnop said:
I got 1/[(2-x)^2]
First off, this thread is almost 9 months old.

Second, my answer agrees exactly with mrkuo's answer. lmnop, how did you get your answer?
 

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