Question about implicit differentiation

Calculus3

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Hi guys, I have 2 questions to ask you: b and the question with second image. Any comments and opinions are appreciate!

I am stuck at some points where I don’t know what to do. I hope someone can clarify me to get solution.

Thank you all!
 

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On your ellipse problem, you calculated y' correctly. Now just plug in your values for x & y and you have dy/dx.
 
Thank you very much for providing your work. We appreciate it. There is, however, a reason that we ask that you not give a list of problems in one thread: the thread quickly becomes a mess as people answer different problems. It is exacerbated when you ask about question b and both problems have a question marked as b. Nor is it helped by telling us “actually is the first image,” a sentence without a subject is literally talking about nothing.

I am making a guess that you are asking about the geometric interpretation of what your formula for the derivative means at x = 3.

Let’s start by asking what real number corresponds to the derivative when x = 3?

So what does that tell us about the line of tangency to the ellipse at x = 3.

What does that tell us about the derivative?

What is the sign of the function’s derivative if 0 < x < 3?

Is there even a function?
 
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