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amorfide Group Title

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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  1. hartnn Group Title
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    heard of implicit differentiation ?

    • one year ago
  2. amorfide Group Title
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    no i have never heard of it

    • one year ago
  3. Kainui Group Title
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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)

    • one year ago
  4. hartnn Group Title
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    u want to diff w..r.t x, right ?

    • one year ago
  5. Kainui Group Title
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    6* not 3x or 3y by the way! lol

    • one year ago
  6. amorfide Group Title
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    yeah rtx

    • one year ago
  7. hartnn Group Title
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    ok, so u know product rule, and chain rule, can u differentiate xy ?

    • one year ago
  8. amorfide Group Title
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    no i can not lol i have never had xy together only y=x or something

    • one year ago
  9. hartnn Group Title
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    but u know product rule right ? take x and y as different functions and diff. xy using product rule

    • one year ago
  10. hartnn Group Title
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    like x'y+xy' and x' = ?

    • one year ago
  11. amorfide Group Title
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    would it be y+x?

    • one year ago
  12. hartnn Group Title
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    umm.....x'=1 right ? so diff. of xy will be y+xy' ok

    • one year ago
  13. amorfide Group Title
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    but isnt y' also 1? so it would be y+x?

    • one year ago
  14. hartnn Group Title
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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 ?

    • one year ago
  15. amorfide Group Title
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    ohhh okay! thank you, that makes more sense

    • one year ago
  16. hartnn Group Title
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    and what will be diff. of y^2 then ?

    • one year ago
  17. amorfide Group Title
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    2y²' ?

    • one year ago
  18. hartnn Group Title
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    since d/dx of x^2 = 2x d/dy of y^2 = 2y dy/dx = 2yy' ok?

    • one year ago
  19. amorfide Group Title
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    okay so the diff of y^3 would be 3y²y' ?

    • one year ago
  20. hartnn Group Title
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    yup

    • one year ago
  21. amorfide Group Title
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    x² + xy + y² = 1 soo 2x+(x+y')+2y'=0 is that right

    • one year ago
  22. hartnn Group Title
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    2nd term ? y+xy'

    • one year ago
  23. amorfide Group Title
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    oops yeah that is what i meant 2x+(y+xy')+2y'=0

    • one year ago
  24. amorfide Group Title
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    2x+(y+xy')+2yy' =0

    • one year ago
  25. hartnn Group Title
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    yes, now find y' from there ?

    • one year ago
  26. amorfide Group Title
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    how do i do that? lol

    • one year ago
  27. amorfide Group Title
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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

    • one year ago
  28. hartnn Group Title
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    2x+(y+xy')+2yy' =0 xy'+2yy' = -2x-y (x+2y)y' = -(2x+y) now ?

    • one year ago
  29. amorfide Group Title
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    (x+2y)y' = -(2x+y) y'=-(2x+y)/(x+2y)

    • one year ago
  30. hartnn Group Title
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    yes :)

    • one year ago
  31. hartnn Group Title
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    wasn't it easy ?

    • one year ago
  32. amorfide Group Title
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    thank you! is that the entire thing finished?

    • one year ago
  33. hartnn Group Title
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    yup., u got your y'

    • one year ago
  34. amorfide Group Title
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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!

    • one year ago
  35. hartnn Group Title
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    welcome ^_^

    • one year ago
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