A community for students.
Here's the question you clicked on:
 0 viewing
amorfide
 3 years ago
okay so just out of curiousity
if i had
x² + xy + y² = 1
how would i differentiate?
amorfide
 3 years ago
okay so just out of curiousity if i had x² + xy + y² = 1 how would i differentiate?

This Question is Closed

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

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

Kainui
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.2u want to diff w..r.t x, right ?

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

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

amorfide
 3 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
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.2umm.....x'=1 right ? so diff. of xy will be y+xy' ok

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

hartnn
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0ohhh okay! thank you, that makes more sense

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

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

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

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

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

amorfide
 3 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
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0(x+2y)y' = (2x+y) y'=(2x+y)/(x+2y)

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

amorfide
 3 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!
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.