amorfide
okay so just out of curiousity
if i had
x² + xy + y² = 1
how would i differentiate?
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hartnn
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heard of implicit differentiation ?
amorfide
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no i have never heard of it
Kainui
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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)
hartnn
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u want to diff w..r.t x, right ?
Kainui
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6* not 3x or 3y by the way! lol
amorfide
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yeah rtx
hartnn
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ok, so u know product rule, and chain rule,
can u differentiate xy ?
amorfide
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no i can not lol
i have never had xy together only y=x or something
hartnn
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but u know product rule right ?
take x and y as different functions and diff. xy using product rule
hartnn
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like x'y+xy'
and x' = ?
amorfide
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would it be y+x?
hartnn
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umm.....x'=1 right ?
so diff. of xy will be y+xy'
ok
amorfide
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but isnt y' also 1? so it would be y+x?
hartnn
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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
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ohhh okay! thank you, that makes more sense
hartnn
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and what will be diff. of y^2 then ?
amorfide
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2y²' ?
hartnn
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since d/dx of x^2 = 2x
d/dy of y^2 = 2y dy/dx = 2yy'
ok?
amorfide
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okay so the diff of y^3 would be 3y²y' ?
hartnn
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yup
amorfide
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x² + xy + y² = 1
soo
2x+(x+y')+2y'=0 is that right
hartnn
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2nd term ?
y+xy'
amorfide
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oops yeah that is what i meant
2x+(y+xy')+2y'=0
amorfide
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2x+(y+xy')+2yy' =0
hartnn
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yes, now find y' from there ?
amorfide
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how do i do that? lol
amorfide
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2x+(y+xy')+2yy' =0
-2x=y+xy' +2yy'
-2x-y=xy'+2yy'
-2x-y/2y=xy'/2y +y'
uhm im stuck
hartnn
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2x+(y+xy')+2yy' =0
xy'+2yy' = -2x-y
(x+2y)y' = -(2x+y)
now ?
amorfide
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(x+2y)y' = -(2x+y)
y'=-(2x+y)/(x+2y)
hartnn
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yes :)
hartnn
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wasn't it easy ?
amorfide
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thank you! is that the entire thing finished?
hartnn
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yup., u got your y'
amorfide
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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
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welcome ^_^