I need help with differentiating the following equation using implicit differentiation:

x^2 - 2xy + y^3 = 6

Question

I need help with differentiating the following equation using implicit differentiation:

x^2 - 2xy + y^3 = 6

anonymous · Answer

do this
d/dx (x^2)
d/dx(2xy)
d/dx(y^3)
d/dx(6)

anonymous · Answer

Right, so that gives me 

2x - 2y - 2y'x + 3y^2y' = 0

correct?

anonymous · Answer

right. Solve for y' and you're done

anonymous · Answer

This is what I get when I solve for y' but apparently its incorrect... 

$$y' = \frac{ 2y - 2x }{ 3y^2 - 2x }$$

anonymous · Answer

You differentiated it right so it must be that you made an algebraic mistake somewhere when solving for y'. check again.

amistre64 · Answer

the algebra seems fine

anonymous · Answer

Really? So do you think that's the correct answer?

amistre64 · Answer

maybe the system they are using thinks it can be reduced

anonymous · Answer

Right... But I also put the equation into an online calculator and it gets ...

$$y' = \frac{ 2x-2y }{ 2x - 3y^2 }$$

amistre64 · Answer

you can factor a 2 out of the top, but i dont see much else for it

anonymous · Answer

I keep looking through my calculations and I still don't see anything wrong

amistre64 · Answer

factoring out a -1/-1 is not that important

amistre64 · Answer

2(x-y) for the top

anonymous · Answer

Does it change the answer when you factor out a -1/-1 ?

amistre64 · Answer

it only changes form since -1/-1 = 1

amistre64 · Answer

(a-b) = -(b-a)

anonymous · Answer

Right, so it wouldn't be a necessary step to take right?

amistre64 · Answer

its not required to me

amistre64 · Answer

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 · Answer

y' = 2(y-x)/(3y^2 - 2x)

anonymous · Answer

That's exactly what I did! So I don't think it should be wrong

amistre64 · Answer

its not wrong according to what you have provided us.

can you give a screen shot or picture?

anonymous · Answer

Of the question?

amistre64 · Answer

perferably yes ...

anonymous · Answer

Sure

amistre64 · Answer

and how many tries do you have to get it 'correct' ?

anonymous · Answer

It's unlimited

amistre64 · Answer

oh that good lol

anonymous · Answer

Haha i know right xD

amistre64 · Answer

screen shot it when you input  

 2(y-x)/(3y^2 - 2x)

anonymous · Answer

kk hold on

anonymous · Answer

Oh wow now its saying that it's correct >.< This is ridiculous lol

amistre64 · Answer

i was going to see if you were missing a paranthesis :)

anonymous · Answer

I'm always cautious of the parentheses XD there was something wrong with the program, I'm sure :D lol

anonymous · Answer

Thanks so much though!

amistre64 · Answer

good luck :)

anonymous · Answer

Thanks! :)