anonymous
  • anonymous
I need help with differentiating the following equation using implicit differentiation: x^2 - 2xy + y^3 = 6
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
do this d/dx (x^2) d/dx(2xy) d/dx(y^3) d/dx(6)
anonymous
  • anonymous
Right, so that gives me 2x - 2y - 2y'x + 3y^2y' = 0 correct?
anonymous
  • anonymous
right. Solve for y' and you're done

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anonymous
  • anonymous
This is what I get when I solve for y' but apparently its incorrect... \[y' = \frac{ 2y - 2x }{ 3y^2 - 2x }\]
anonymous
  • anonymous
You differentiated it right so it must be that you made an algebraic mistake somewhere when solving for y'. check again.
amistre64
  • amistre64
the algebra seems fine
anonymous
  • anonymous
Really? So do you think that's the correct answer?
amistre64
  • amistre64
maybe the system they are using thinks it can be reduced
anonymous
  • anonymous
Right... But I also put the equation into an online calculator and it gets ... \[y' = \frac{ 2x-2y }{ 2x - 3y^2 }\]
amistre64
  • amistre64
you can factor a 2 out of the top, but i dont see much else for it
anonymous
  • anonymous
I keep looking through my calculations and I still don't see anything wrong
amistre64
  • amistre64
factoring out a -1/-1 is not that important
amistre64
  • amistre64
2(x-y) for the top
anonymous
  • anonymous
Does it change the answer when you factor out a -1/-1 ?
amistre64
  • amistre64
it only changes form since -1/-1 = 1
amistre64
  • amistre64
(a-b) = -(b-a)
anonymous
  • anonymous
Right, so it wouldn't be a necessary step to take right?
amistre64
  • amistre64
its not required to me
amistre64
  • amistre64
x^2 - 2xy + y^3 = 6 2x x' - (2x'y+2xy') + 3y^2 y' = 0 x' = dx/dx = 1 2x - 2y -2x y' + 3y^2 y' = 0 2x - 2y + (3y^2-2x) y' = 0 2(x -y) + (3y^2-2x) y' = 0
amistre64
  • amistre64
y' = 2(y-x)/(3y^2 - 2x)
anonymous
  • anonymous
That's exactly what I did! So I don't think it should be wrong
amistre64
  • amistre64
its not wrong according to what you have provided us. can you give a screen shot or picture?
anonymous
  • anonymous
Of the question?
amistre64
  • amistre64
perferably yes ...
anonymous
  • anonymous
amistre64
  • amistre64
and how many tries do you have to get it 'correct' ?
anonymous
  • anonymous
It's unlimited
amistre64
  • amistre64
oh that good lol
anonymous
  • anonymous
Haha i know right xD
amistre64
  • amistre64
screen shot it when you input 2(y-x)/(3y^2 - 2x)
anonymous
  • anonymous
kk hold on
anonymous
  • anonymous
Oh wow now its saying that it's correct >.< This is ridiculous lol
amistre64
  • amistre64
i was going to see if you were missing a paranthesis :)
anonymous
  • anonymous
I'm always cautious of the parentheses XD there was something wrong with the program, I'm sure :D lol
anonymous
  • anonymous
Thanks so much though!
amistre64
  • amistre64
good luck :)
anonymous
  • anonymous
Thanks! :)

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