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

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In summary, the conversation is about finding the derivative of x*sqrt[x/(2-x)] and whether multiple solutions provided by different individuals are correct. The proper solution involves using the product rule, chain rule, and quotient rule in the correct order, and the final answer is 1/[(2-x)^2].
  • #1
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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  • #2
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"? :)
 
  • #3
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
 
  • #4
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!
 
  • #5
I got 1/[(2-x)^2]
 
  • #6
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?
 

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

What is a simple derivative check?

A simple derivative check is a method used to verify the accuracy of a mathematical derivative. It involves taking the derivative of a function using basic calculus rules and comparing it to the derivative calculated using numerical methods. If the two derivatives are close in value, it can be assumed that the derivative has been correctly calculated.

Why is a simple derivative check important?

A simple derivative check is important because it allows us to verify the accuracy of our calculations. Small errors in a derivative can lead to significant errors in the final result, so it is crucial to ensure the accuracy of this calculation.

What are the steps involved in a simple derivative check?

The steps involved in a simple derivative check are:

  1. Calculate the derivative of the function using basic calculus rules.
  2. Choose a small value for the change in the independent variable, h.
  3. Calculate the derivative using numerical methods, such as the forward or central difference method.
  4. Compare the two derivatives and check for consistency.

What are some common sources of error in a simple derivative check?

Common sources of error in a simple derivative check include choosing an inappropriate value for h, rounding errors in calculations, and errors in the original function used to calculate the derivative.

When should a simple derivative check be used?

A simple derivative check should be used whenever there is a need to verify the accuracy of a derivative calculation. This can be in various fields including physics, engineering, economics, and more. It is also useful when writing computer programs that involve derivatives, as it can help catch any coding errors.

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