Find the equation of the tangent line of the curve

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The discussion focuses on finding the equation of the tangent line to the curve defined by xy² + 2/y = 4 at the point (2,1). The correct slope of the tangent line is derived using implicit differentiation, resulting in dy/dx = -y²/(2xy - 2/y²). Participants highlight errors in applying the product and chain rules, emphasizing the importance of careful differentiation steps. The conversation also touches on the need for better understanding of calculus fundamentals and the value of supplementary learning resources, such as textbooks and online courses. Mastery of basic derivative rules is deemed essential for solving more complex problems effectively.
  • #31
Alright, well I just got both. Can't hurt to have more.
 
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  • #32
Schaus said:
So I got the wrong one? Crap
I don't know.
 
  • #33
Schaus said:
I learn more easily from seeing something done.
Certainly it's easier to understand a problem by seeing a solution to it, but I don't necessarily believe that you're actually learning much of anything. A good textbook will have plenty of examples, but the learning comes when you actually do the work for a problem. Part of the learning process is in making false starts and going along branches that don't lead anywhere. This thread is (I hope) a good example of what I'm talking about.
 

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