SOLUTION: Given the equation x^2+y^2=9 , express y explicitly and calculate the derivative.

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Question 1193267: Given the equation x^2+y^2=9 , express y explicitly and calculate the
derivative.
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Given the equation x^2+y^2=9 , express y explicitly and calculate the
derivative.
=====================================
Not clear what you want to do.
But,
x^2+y^2=9
Differentiate ---> 2x*dx + 2y*dy = 0
x*dx = -y*dy
dy/dx = -x/y
The slope of the tangent to circle at any point is -x/y

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Given the equation x%5E2%2By%5E2=9 , express y explicitly and calculate the
derivative.
x%5E2%2By%5E2=9
y%5E2=9-x%5E2
y=sqrt%289-x%5E2%29

calculate the derivative:

%28d%2Fdx%29%28sqrt%289-x%5E2%29%29

%28d%2Fdx%29%28%289-x%5E2%29%5E%281%2F2%29%29............apply the chain rule

=%281%2F%282sqrt%289-x%5E2%29%29%29%28d%2Fdx%29%289-x%5E2%29

=%281%2F%282sqrt%289-x%5E2%29%29%29%28-2x%29

=%281%2F%28sqrt%289-x%5E2%29%29%29%28-x%29.....factor 9-x%5E2

= -x%2Fsqrt%28%283+-+x%29%283%2Bx%29%29

= -x%2F%28sqrt%283+-+x%29+sqrt%28x+%2B+3%29%29
so,
y'%28x%29+=+-x%2F%28sqrt%283+-+x%29+sqrt%28x+%2B+3%29%29