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amorfide
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okay so just out of curiousity
if i had
x² + xy + y² = 1
how would i differentiate?
 2 years ago
 2 years ago
amorfide Group Title
okay so just out of curiousity if i had x² + xy + y² = 1 how would i differentiate?
 2 years ago
 2 years ago

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hartnn Group TitleBest ResponseYou've already chosen the best response.2
heard of implicit differentiation ?
 2 years ago

amorfide Group TitleBest ResponseYou've already chosen the best response.0
no i have never heard of it
 2 years ago

Kainui Group TitleBest ResponseYou've already chosen the best response.1
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)
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
u want to diff w..r.t x, right ?
 2 years ago

Kainui Group TitleBest ResponseYou've already chosen the best response.1
6* not 3x or 3y by the way! lol
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
ok, so u know product rule, and chain rule, can u differentiate xy ?
 2 years ago

amorfide Group TitleBest ResponseYou've already chosen the best response.0
no i can not lol i have never had xy together only y=x or something
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
but u know product rule right ? take x and y as different functions and diff. xy using product rule
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
like x'y+xy' and x' = ?
 2 years ago

amorfide Group TitleBest ResponseYou've already chosen the best response.0
would it be y+x?
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
umm.....x'=1 right ? so diff. of xy will be y+xy' ok
 2 years ago

amorfide Group TitleBest ResponseYou've already chosen the best response.0
but isnt y' also 1? so it would be y+x?
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
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 ?
 2 years ago

amorfide Group TitleBest ResponseYou've already chosen the best response.0
ohhh okay! thank you, that makes more sense
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
and what will be diff. of y^2 then ?
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
since d/dx of x^2 = 2x d/dy of y^2 = 2y dy/dx = 2yy' ok?
 2 years ago

amorfide Group TitleBest ResponseYou've already chosen the best response.0
okay so the diff of y^3 would be 3y²y' ?
 2 years ago

amorfide Group TitleBest ResponseYou've already chosen the best response.0
x² + xy + y² = 1 soo 2x+(x+y')+2y'=0 is that right
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
2nd term ? y+xy'
 2 years ago

amorfide Group TitleBest ResponseYou've already chosen the best response.0
oops yeah that is what i meant 2x+(y+xy')+2y'=0
 2 years ago

amorfide Group TitleBest ResponseYou've already chosen the best response.0
2x+(y+xy')+2yy' =0
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
yes, now find y' from there ?
 2 years ago

amorfide Group TitleBest ResponseYou've already chosen the best response.0
how do i do that? lol
 2 years ago

amorfide Group TitleBest ResponseYou've already chosen the best response.0
2x+(y+xy')+2yy' =0 2x=y+xy' +2yy' 2xy=xy'+2yy' 2xy/2y=xy'/2y +y' uhm im stuck
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
2x+(y+xy')+2yy' =0 xy'+2yy' = 2xy (x+2y)y' = (2x+y) now ?
 2 years ago

amorfide Group TitleBest ResponseYou've already chosen the best response.0
(x+2y)y' = (2x+y) y'=(2x+y)/(x+2y)
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
wasn't it easy ?
 2 years ago

amorfide Group TitleBest ResponseYou've already chosen the best response.0
thank you! is that the entire thing finished?
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
yup., u got your y'
 2 years ago

amorfide Group TitleBest ResponseYou've already chosen the best response.0
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!
 2 years ago
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