Can Someone Explain How to Differentiate 3x^2 y^2 with Respect to y?

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Discussion Overview

The discussion revolves around the differentiation of the expression 3x²y² with respect to y, focusing on the application of partial differentiation. Participants explore the correct approach to differentiate the function and clarify their understanding of the process.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant asks for clarification on how to differentiate 3x²y² with respect to y, expressing uncertainty about the process.
  • Another participant explains that to differentiate 3x²y² with respect to y, one should treat x as a constant, leading to the derivative 6x²y.
  • A later reply indicates confusion about the original question, suggesting that the answer provided may not correspond to the correct expression being differentiated.
  • Another participant corrects their earlier statement, indicating that they misread the original function and acknowledges that the differentiation process is understood.
  • There is a suggestion that if the expression were z = x²y³, then the derivative would match the quoted answer, indicating a potential misunderstanding of the original function.
  • One participant humorously notes the oddity of a derivative equating to the original function without involving the exponential function, hinting at the peculiarity of the situation.

Areas of Agreement / Disagreement

Participants express confusion and uncertainty regarding the correct function to differentiate, leading to multiple interpretations and no clear consensus on the original question or its answer.

Contextual Notes

Participants display varying levels of understanding about partial differentiation, and there are indications of miscommunication regarding the function being differentiated, which complicates the discussion.

cabellos
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Iv forgotten the basics of this. How do we go about differentiating 3x^2 y^2 w.r.t y? I know the answer is 3x^2 y^2 but could someone explain this for me please?
 
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cabellos said:
Iv forgotten the basics of this. How do we go about differentiating 3x^2 y^2 w.r.t y? I know the answer is 3x^2 y^2 but could someone explain this for me please?

You want to perform \frac{\partial}{\partial y}(3x^2y^2).

You would simply treat the function of x as a constant and differentiate y normally, thus yielding 6x^2y.

However, this is not what your answer is, so I wonder whether it is the correct question?
 
ooops I am getting myself all confused now. I know how to do partial differentiation after all. I was reading the wrong solution as the question was z = x^2 y^2 and ofcourse dz/dy would = 3x^2 y^2 !
 
cabellos said:
ooops I am getting myself all confused now. I know how to do partial differentiation after all. I was reading the wrong solution as the question was z = x^2 y^2 and ofcourse dz/dy would = 3x^2 y^2 !

Erm.. no it wouldn't.

Unless you mean z=x2y3, in which case, dz/dy would be the answer you quoted.
 
i need some sleep! Yeah i meant y^3 lol !
 
Its a big warning flag when the derivative is equal to the original function and doesn't involve e in it...
 

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