anonymous
  • anonymous
use implicit differentiation to find dy/dx - 2xy-y^2= 1 can someone explain step by step with formulas explaining in detail.
Mathematics
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SOLVED
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chestercat
  • chestercat
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bahrom7893
  • bahrom7893
Let me call dy/dx y'
bahrom7893
  • bahrom7893
use product rule for -2xy and power rule for -y^2: -2x*y' + y*(-2) - 2y*y' = 0
bahrom7893
  • bahrom7893
-2xy' - 2y - 2yy' = 0, divide everything by -2: xy' + y + yy' = 0

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bahrom7893
  • bahrom7893
now move y to the right side: xy' + yy' = -y
anonymous
  • anonymous
you lost the =1
bahrom7893
  • bahrom7893
where?
anonymous
  • anonymous
-2xy-y^2 = 1 is original problem right?
bahrom7893
  • bahrom7893
yeah, but derivative of a constant is 0!
anonymous
  • anonymous
gotcha
anonymous
  • anonymous
what is the formula for implicit differentiation ?
bahrom7893
  • bahrom7893
now move y to the right side: xy' + yy' = -y take y' out: y'(x+y) = -y
bahrom7893
  • bahrom7893
there is no formula, u use a combination of several formulas
anonymous
  • anonymous
oh ah...ok let me look and little by little look into what u wrote to understand
bahrom7893
  • bahrom7893
y' = dy/dx = -y/(x+y). Fan me if I helped, thanx! =)

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