Expert: Paul Klarreich - 5/24/2008

Question
Given the equation 5x^(2)-6x+5y^(2)=16, find dy/dx.  What is its value at points (2,2) and (1,-1)?

Answer
Questioner:   harman
Category:  Calculus
Private:  No
 
Subject:  ap calculus, changing of variables
Question:  Given the equation 5x^(2)-6x+5y^(2)=16, find dy/dx.  What is its value at points (2,2) and (1,-1)?
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Hi, Harman,

5x^2 - 6x + 5y^2 = 16

Use Implicit differentiation:

10x - 6 + 10y dy/dx = 0

5x - 3 + 5y dy/dx = 0

5y dy/dx = 3 - 5x

       3 - 5x
dy/dx = -------
         5y

Now put in your (2,2) and your (1,-1) and you have your answers.

Note: You sent a second question.  As soon as I see you have picked up this answer, I'll get to that one.