okay so just out of curiousity
if i had
x² + xy + y² = 1
how would i differentiate?

- amorfide

okay so just out of curiousity
if i had
x² + xy + y² = 1
how would i differentiate?

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- hartnn

heard of implicit differentiation ?

- amorfide

no i have never heard of it

- Kainui

you really just use the chain rule. Most of the time the derivative with respect to x is 1, so you don't think about the derivative of 3x^2 being 3x*1, but when you do implicit differentiation you take the derivative of 3y^2 to be 3y*(dy/dx)

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## More answers

- hartnn

u want to diff w..r.t x, right ?

- Kainui

6* not 3x or 3y by the way! lol

- amorfide

yeah rtx

- hartnn

ok, so u know product rule, and chain rule,
can u differentiate xy ?

- amorfide

no i can not lol
i have never had xy together only y=x or something

- hartnn

but u know product rule right ?
take x and y as different functions and diff. xy using product rule

- hartnn

like x'y+xy'
and x' = ?

- amorfide

would it be y+x?

- hartnn

umm.....x'=1 right ?
so diff. of xy will be y+xy'
ok

- amorfide

but isnt y' also 1? so it would be y+x?

- hartnn

y' would have been 1 if you would have diff. w.r.t y
as in d/dy of y =1
but here you are differentiating w.r.t x
do its diff. would be
dy/dx that is y'
makes sense ?

- amorfide

ohhh okay! thank you, that makes more sense

- hartnn

and what will be diff. of y^2 then ?

- amorfide

2y²' ?

- hartnn

since d/dx of x^2 = 2x
d/dy of y^2 = 2y dy/dx = 2yy'
ok?

- amorfide

okay so the diff of y^3 would be 3y²y' ?

- hartnn

yup

- amorfide

x² + xy + y² = 1
soo
2x+(x+y')+2y'=0 is that right

- hartnn

2nd term ?
y+xy'

- amorfide

oops yeah that is what i meant
2x+(y+xy')+2y'=0

- amorfide

2x+(y+xy')+2yy' =0

- hartnn

yes, now find y' from there ?

- amorfide

how do i do that? lol

- amorfide

2x+(y+xy')+2yy' =0
-2x=y+xy' +2yy'
-2x-y=xy'+2yy'
-2x-y/2y=xy'/2y +y'
uhm im stuck

- hartnn

2x+(y+xy')+2yy' =0
xy'+2yy' = -2x-y
(x+2y)y' = -(2x+y)
now ?

- amorfide

(x+2y)y' = -(2x+y)
y'=-(2x+y)/(x+2y)

- hartnn

yes :)

- hartnn

wasn't it easy ?

- amorfide

thank you! is that the entire thing finished?

- hartnn

yup., u got your y'

- amorfide

easier than i thought, thank you, i was just curious how to do a question like this, it isn't needed :P
you are awesome!

- hartnn

welcome ^_^

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