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

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SUMMARY

The discussion focuses on differentiating the function 3x²y² with respect to y using partial differentiation. The correct derivative is 6x²y, achieved by treating x as a constant while differentiating y. The confusion arose when participants mistakenly referenced the function as z = x²y² instead of the correct form. Clarification was provided that if the function were z = x²y³, the derivative would indeed be 3x²y².

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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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