- #1
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[tex]$ 4xy = y^2 + 2 \ln x[/tex]
How do I differentiate that?
How do I differentiate that?
How to differentiate the expression 4xy = y^2 + 2ln(x)
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Homework Help Overview
The discussion revolves around differentiating the expression 4xy = y^2 + 2ln(x), focusing on the methods of differentiation applicable to implicit functions.
Discussion Character
- Mixed
Approaches and Questions Raised
- Participants discuss the use of implicit differentiation and express confusion regarding its application. Some suggest rewriting the equation to apply the quadratic formula as an alternative approach. Questions arise about the necessity of using different methods and the rationale behind teaching certain techniques.
Discussion Status
There is an exploration of different methods for differentiation, with some participants providing guidance on implicit differentiation while others express a lack of familiarity with the concept. The discussion reflects a mix of attempts to clarify methods and question the pedagogical choices involved.
Contextual Notes
Some participants indicate constraints in their learning, specifically mentioning unfamiliarity with implicit differentiation and questioning the traditional methods taught in their coursework.
- #2
ToxicBug
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Use implicit differentiation.
4y + 4xy' = 2yy' + 2/x
y'(4x - 2y) = 2/x - 4y
y' = (2/x - 4y)/(4x - 2y)
4y + 4xy' = 2yy' + 2/x
y'(4x - 2y) = 2/x - 4y
y' = (2/x - 4y)/(4x - 2y)
- #3
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ToxicBug said:
Sorry, but I've not learned implicit differentiation. Haven't even heard of it.- #4
ToxicBug
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Then I don't know how you would isolate y in that to solve it the normal way.
- #5
t!m
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Rewrite the expression as [tex]y^2 - 4xy + 2 \ln x = 0[/tex] and use the quadratic formula to find y in terms of x. Then derive.
- #6
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Got it. Thank you.
- #7
ToxicBug
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Why do teachers ask their students to do something like that when it can be solved using a more proficient technique?t!m said:
- #8
Hurkyl
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It's always reassuring to see that two drastically different methods yield the same results.
Also, doing this problem both ways will allow students to greater appreciate implicit differentiation, once they see how much work it can save.
Also, doing this problem both ways will allow students to greater appreciate implicit differentiation, once they see how much work it can save.