## amorfide 3 years ago okay so just out of curiousity if i had x² + xy + y² = 1 how would i differentiate?

1. hartnn

heard of implicit differentiation ?

2. amorfide

no i have never heard of it

3. Kainui

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)

4. hartnn

u want to diff w..r.t x, right ?

5. Kainui

6* not 3x or 3y by the way! lol

6. amorfide

yeah rtx

7. hartnn

ok, so u know product rule, and chain rule, can u differentiate xy ?

8. amorfide

no i can not lol i have never had xy together only y=x or something

9. hartnn

but u know product rule right ? take x and y as different functions and diff. xy using product rule

10. hartnn

like x'y+xy' and x' = ?

11. amorfide

would it be y+x?

12. hartnn

umm.....x'=1 right ? so diff. of xy will be y+xy' ok

13. amorfide

but isnt y' also 1? so it would be y+x?

14. hartnn

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 ?

15. amorfide

ohhh okay! thank you, that makes more sense

16. hartnn

and what will be diff. of y^2 then ?

17. amorfide

2y²' ?

18. hartnn

since d/dx of x^2 = 2x d/dy of y^2 = 2y dy/dx = 2yy' ok?

19. amorfide

okay so the diff of y^3 would be 3y²y' ?

20. hartnn

yup

21. amorfide

x² + xy + y² = 1 soo 2x+(x+y')+2y'=0 is that right

22. hartnn

2nd term ? y+xy'

23. amorfide

oops yeah that is what i meant 2x+(y+xy')+2y'=0

24. amorfide

2x+(y+xy')+2yy' =0

25. hartnn

yes, now find y' from there ?

26. amorfide

how do i do that? lol

27. amorfide

2x+(y+xy')+2yy' =0 -2x=y+xy' +2yy' -2x-y=xy'+2yy' -2x-y/2y=xy'/2y +y' uhm im stuck

28. hartnn

2x+(y+xy')+2yy' =0 xy'+2yy' = -2x-y (x+2y)y' = -(2x+y) now ?

29. amorfide

(x+2y)y' = -(2x+y) y'=-(2x+y)/(x+2y)

30. hartnn

yes :)

31. hartnn

wasn't it easy ?

32. amorfide

thank you! is that the entire thing finished?

33. hartnn

34. amorfide

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!

35. hartnn

welcome ^_^