anonymous
  • anonymous
dy/dx of xy=(x^2)+(y^2)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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starwars18
  • starwars18
x'y+xy' = 2xx' + 2yy'
anonymous
  • anonymous
The answer posted for this problem is (2x-y)/(x-2y)
phi
  • phi
can you do the implicit differentiation ? of for example \[ \frac{d}{dy}(xy) \]

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Landon34
  • Landon34
just use http://www.geteasysolution.com/
anonymous
  • anonymous
Its for a final i just wanted to understand it
anonymous
  • anonymous
I got the right answer i just wanted to know how that one guy got x'y+xy' = 2xx' + 2yy'
anonymous
  • anonymous
Since i was able to manipulate it to the correct answer
phi
  • phi
by the product rule \[ \frac{d}{dx}(xy) = x \frac{d}{dx}y + y \frac{d}{dx}x \\ = x\frac{dy}{dx}+ y \]
anonymous
  • anonymous
Thanks!
phi
  • phi
and the right-hand side is \[ \frac{d}{dx}x^2 + \frac{d}{dx}y^2 \\= 2 x + 2y \frac{dy}{dx}\]
anonymous
  • anonymous
I think i just over thought it
phi
  • phi
ok, and to finish it (and using y' for dy/dx) btw x' in this case would mean dx/dx = 1 xy' + y = 2x + 2y y' x y' - 2y y' = 2x -y (x - 2y) y' = 2x -y and \[ y' = \frac{2x-y}{x-2y} \]

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