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

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

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

Kainui
 2 years ago
Best ResponseYou've already chosen the best response.1you 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
 2 years ago
Best ResponseYou've already chosen the best response.2u want to diff w..r.t x, right ?

Kainui
 2 years ago
Best ResponseYou've already chosen the best response.16* not 3x or 3y by the way! lol

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

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

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

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

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

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2y' 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
 2 years ago
Best ResponseYou've already chosen the best response.0ohhh okay! thank you, that makes more sense

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

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

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

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

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

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

amorfide
 2 years ago
Best ResponseYou've already chosen the best response.02x+(y+xy')+2yy' =0 2x=y+xy' +2yy' 2xy=xy'+2yy' 2xy/2y=xy'/2y +y' uhm im stuck

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.22x+(y+xy')+2yy' =0 xy'+2yy' = 2xy (x+2y)y' = (2x+y) now ?

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

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

amorfide
 2 years ago
Best ResponseYou've already chosen the best response.0easier than i thought, thank you, i was just curious how to do a question like this, it isn't needed :P you are awesome!
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