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

[hanelliot]

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?

 

[mrkuo]

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"? :)

 

[Mark44]

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

 

[hanelliot]

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!

 

[lmnop]

I got 1/[(2-x)^2]

 

[Mark44]

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?