- #1
Pondera
- 13
- 0
Implicit Differentiation with Sin
- Thread starter Pondera
- Start date
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Homework Help Overview
The discussion revolves around the application of implicit differentiation, specifically involving the differentiation of a product of functions, as indicated by the expression xy². Participants are exploring the correct application of differentiation rules in this context.
Discussion Character
- Mathematical reasoning, Assumption checking
Approaches and Questions Raised
- Participants discuss the application of the product rule in differentiation, with one participant initially misunderstanding its use. Questions arise regarding the manipulation of terms in the differentiation process, particularly concerning multiplication and division in the final steps.
Discussion Status
The discussion has progressed with participants providing feedback on each other's attempts. Some guidance has been offered regarding the correct application of differentiation rules, and there is acknowledgment of errors in the approach. Multiple interpretations of the steps taken are being explored, but no explicit consensus has been reached.
Contextual Notes
There is an indication of informal communication among participants, with expressions of uncertainty and humor about the differentiation process. The original poster's initial misunderstanding of the product rule is noted, as well as the subsequent corrections discussed.
- #2
jgens
Gold Member
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It looks like you're not applying the product rule properly when differentiating xy^2. d(xy^2) = y^2 + 2xyy'
- #3
Pondera
- 13
- 0
I wasn't using the product rule at all. Thank you for that! Haha.
I tried it again and got:
Line by line:
7= cos(xy^2)(y^2+2xyy')
7/ cos(xy^2) = (y^2+2xyy')
7/ cos(xy^2) - y^2 = 2xyy'
(7/ cos(xy^2) - y^2)(2xy) = y'
I tried it again and got:
Line by line:
7= cos(xy^2)(y^2+2xyy')
7/ cos(xy^2) = (y^2+2xyy')
7/ cos(xy^2) - y^2 = 2xyy'
(7/ cos(xy^2) - y^2)(2xy) = y'
- #4
gabbagabbahey
Homework Helper
Gold Member
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On your last step, why are you multiplying by 2xy?...Shouldn't you be dividing instead?
- #5
Pondera
- 13
- 0
Yeah, it should be divided by our multiplied by (1/2xy). I'm not sure why I did that. :P
The rest of it looks okay though?
The rest of it looks okay though?
- #6
gabbagabbahey
Homework Helper
Gold Member
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the rest looks fine 
- #7
Pondera
- 13
- 0
WOOO! It was right! Thank you very much, jgens and gabba.
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