I need help with differentiating the following equation using implicit differentiation:
x^2 - 2xy + y^3 = 6

- anonymous

- Stacey Warren - Expert brainly.com

Hey! We 've verified this expert answer for you, click below to unlock the details :)

- schrodinger

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

- anonymous

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

- anonymous

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

- anonymous

right. Solve for y' and you're done

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- anonymous

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

- anonymous

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

- amistre64

the algebra seems fine

- anonymous

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

- amistre64

maybe the system they are using thinks it can be reduced

- anonymous

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

- amistre64

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

- anonymous

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

- amistre64

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

- amistre64

2(x-y) for the top

- anonymous

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

- amistre64

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

- amistre64

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

- anonymous

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

- amistre64

its not required to me

- 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

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

- anonymous

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

- amistre64

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

- anonymous

Of the question?

- amistre64

perferably yes ...

- anonymous

Sure

##### 1 Attachment

- amistre64

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

- anonymous

It's unlimited

- amistre64

oh that good lol

- anonymous

Haha i know right xD

- amistre64

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

- anonymous

kk hold on

- anonymous

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

##### 1 Attachment

- amistre64

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

- anonymous

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

- anonymous

Thanks so much though!

- amistre64

good luck :)

- anonymous

Thanks! :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.