anonymous
  • anonymous
Find the equation of the tangent line: yx^2+xy^2=6, (1, 2). Can anyone explain the steps of implicit differentiation?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
y'x^2+y(2x)+x(2yy')+y^2=0
anonymous
  • anonymous
Thats the first step right?
anonymous
  • anonymous
y'(x^2+2xy)=-(2xy+y^2) y'=-y(2x+y)/x(x+2y)

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anonymous
  • anonymous
m=y'(at (1,2))=-6/5
anonymous
  • anonymous
tangent line is y-2=-6/5(x-1)
anonymous
  • anonymous
On the key it says the slope is -8/5
anonymous
  • anonymous
oh mistake in computations
anonymous
  • anonymous
-8/5 is the right ans
anonymous
  • anonymous
So implicit differentiation, can you quickly verbally go through it, what steps do you do?
anonymous
  • anonymous
for yx^2 use product rule (derivative of y)x^2+(derivative of x^2) y
anonymous
  • anonymous
y'x^2+2xy....clear?
anonymous
  • anonymous
similar for the second term
anonymous
  • anonymous
OHHHHH!!!! I SEEEEEEE!!!!
anonymous
  • anonymous
THANK YOU SO MUCH! I really appreciate it :D
anonymous
  • anonymous
u welcome:)

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