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

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hartnnBest ResponseYou've already chosen the best response.2
heard of implicit differentiation ?
 one year ago

amorfideBest ResponseYou've already chosen the best response.0
no i have never heard of it
 one year ago

KainuiBest 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)
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
u want to diff w..r.t x, right ?
 one year ago

KainuiBest ResponseYou've already chosen the best response.1
6* not 3x or 3y by the way! lol
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
ok, so u know product rule, and chain rule, can u differentiate xy ?
 one year ago

amorfideBest ResponseYou've already chosen the best response.0
no i can not lol i have never had xy together only y=x or something
 one year ago

hartnnBest 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
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
like x'y+xy' and x' = ?
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
umm.....x'=1 right ? so diff. of xy will be y+xy' ok
 one year ago

amorfideBest ResponseYou've already chosen the best response.0
but isnt y' also 1? so it would be y+x?
 one year ago

hartnnBest 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 ?
 one year ago

amorfideBest ResponseYou've already chosen the best response.0
ohhh okay! thank you, that makes more sense
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
and what will be diff. of y^2 then ?
 one year ago

hartnnBest 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?
 one year ago

amorfideBest ResponseYou've already chosen the best response.0
okay so the diff of y^3 would be 3y²y' ?
 one year ago

amorfideBest ResponseYou've already chosen the best response.0
x² + xy + y² = 1 soo 2x+(x+y')+2y'=0 is that right
 one year ago

amorfideBest ResponseYou've already chosen the best response.0
oops yeah that is what i meant 2x+(y+xy')+2y'=0
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
yes, now find y' from there ?
 one year ago

amorfideBest ResponseYou've already chosen the best response.0
how do i do that? lol
 one year ago

amorfideBest 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
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
2x+(y+xy')+2yy' =0 xy'+2yy' = 2xy (x+2y)y' = (2x+y) now ?
 one year ago

amorfideBest ResponseYou've already chosen the best response.0
(x+2y)y' = (2x+y) y'=(2x+y)/(x+2y)
 one year ago

amorfideBest ResponseYou've already chosen the best response.0
thank you! is that the entire thing finished?
 one year ago

amorfideBest 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!
 one year ago
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