Implicit differentiation question

Click For Summary

Discussion Overview

The discussion revolves around the application of implicit differentiation to the equation 2xy8 + 7xy = 27 at the point (3,1). Participants express confusion over obtaining different answers and seek clarification on the correct approach to the problem.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant expresses frustration over receiving different answers and requests clarification on the problem being solved.
  • Another participant questions the lack of a clear question, suggesting that verifying whether (3,1) satisfies the equation could be a basic arithmetic task.
  • A third participant provides an implicit differentiation approach, deriving the equation 2y8 + 16xy7y' + 7y + 7xy' = 0 and calculating y' at the point (3,1) to be -3/23.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the original question or the correct method to apply. There are competing views on whether the problem is simply verifying a point or performing implicit differentiation.

Contextual Notes

There is ambiguity regarding the specific question being addressed, and assumptions about the problem's requirements are not clearly stated. The mathematical steps provided by participants may depend on interpretations of the original problem.

rcurrie
Messages
1
Reaction score
0
Help! Keep running this and getting different answers, and none are right.

2xy^8 + 7xy = 27 at the point (3,1)
 
Physics news on Phys.org
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?
 

Similar threads

Undergrad Questions about implicit differentiation?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Understanding a quote about implicit differentiation
  • · Replies 4 ·
Replies
4
Views
1K
MHB Can Implicit Differentiation Be Done by Separation of Variables?
  • · Replies 2 ·
Replies
2
Views
1K
High School Implicit differentiation or just explicit?
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Digging deeper into (implicit) differentiation and integration
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad Why Do Implicit Differentiation Results Differ When Multiplying by x or y?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Implicit Differentiation: Differentiating in Terms of X
  • · Replies 7 ·
Replies
7
Views
3K
MHB Implicit Differentiation to find equation of a tangent line
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Basic implicit differentiation question
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad How is implicit differentiation performed in calculus?
  • · Replies 11 ·
Replies
11
Views
2K