How to Derive Using the Chain Rule for 2x^2+5xy-y^2=1?

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SUMMARY

The discussion focuses on deriving the derivative \(\frac{dy}{dx}\) for the implicit function defined by the equation \(2x^2 + 5xy - y^2 = 1\). The initial attempt yielded the expression \(\frac{2y - 4x}{5x}\), which was identified as incorrect. Participants emphasized the importance of showing the steps taken to arrive at a solution to facilitate accurate feedback and correction.

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  • Understanding of implicit differentiation
  • Familiarity with the Chain Rule in calculus
  • Basic algebraic manipulation skills
  • Knowledge of derivatives and their notation
NEXT STEPS
  • Review implicit differentiation techniques
  • Study the Chain Rule for derivatives in calculus
  • Practice solving implicit equations
  • Explore examples of derivatives involving multiple variables
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Students studying calculus, particularly those focusing on implicit differentiation and the Chain Rule, as well as educators seeking to clarify these concepts for learners.

lemonlee
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Homework Statement


2x^2+5xy-y^2=1


Homework Equations


d/dx(f(u)x))=df/du * du/dx


The Attempt at a Solution



i got (2y-4x)/5x but I'm almost certain that its wrong...can anyone help me?
 
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lemonlee said:
i got (2y-4x)/5x but I'm almost certain that its wrong...can anyone help me?

Assuming that you are trying to find [tex]\frac{dy}{dx}[/tex] (you didn't actually tell us what you are trying to calculate!), then it is wrong...However, I can't tell you what you did wrong since you haven't shown me what you did to get your answer...if you do that, I'll be able to help you :wink:
 

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