Implicit differentiation question

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SUMMARY

The discussion centers on the implicit differentiation of the equation 2xy8 + 7xy = 27 at the point (3,1). The correct implicit differentiation yields the derivative y' = -3/23. Participants clarified the problem and provided step-by-step calculations to validate that (3,1) satisfies the original equation. The thread emphasizes the importance of clear problem statements in mathematical discussions.

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rcurrie
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Help! Keep running this and getting different answers, and none are right.

2xy^8 + 7xy = 27 at the point (3,1)
 
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rcurrie said:
Help! Keep running this and getting different answers, and none are right.

2xy^8 + 7xy = 27 at the point (3,1)
Can you post the different answers with the respected work?

Thanks
Cbarker1
 
rcurrie said:
Help! Keep running this and getting different answers, and none are right.

2xy^8 + 7xy = 27 at the point (3,1)
Answers to what question? There is no question or problem here!

IF the problem is "show that (3,1) satifies 2xy^8+ 7xy= 27" or "show that (3, 1) lies on the graph of 2xy^8+ 7xy= 27" then it is basic integer arithmetic.

2(3)(1)^8= 2(3)= 6.
7(3)(1)= 7(3)= 21.

What is the sum of 6 and 21?
 
rcurrie said:
Help! Keep running this and getting different answers, and none are right.

2xy^8 + 7xy = 27 at the point (3,1)
The thread title mentions implicit differentiation. So, differentiate implicitly: $$2y^8 + 16xy^7y' + 7y + 7xy' = 0.$$ At the point $(3,1)$ that becomes $2 + 48y' + 7 + 21y' = 0$. so $69y' + 9 = 0$. That gives $y' = -\dfrac3{23}$. Is that the answer you are looking for?
 

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