MHB Implicit differentiation question

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The discussion revolves around finding the derivative of the equation 2xy^8 + 7xy = 27 at the point (3,1) using implicit differentiation. Participants clarify that the initial confusion stems from not clearly stating the problem, which should confirm that (3,1) satisfies the equation. The implicit differentiation yields the derivative as y' = -3/23 after substituting the point into the differentiated equation. This result addresses the original request for help with implicit differentiation. The thread emphasizes the importance of clear problem statements in mathematical discussions.
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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