Question

Please Help! MEDAL WILL BE REWARDED!
Find dy/dx by implicit differentiation.
x^2(y) + y^2(x) = -2

Answer 1

what have you attempted?

Answer 2

ive gotten to y'=(y(2x+y))/(x(x+2y))

Answer 3

x^2(y) + y^2(x) = -2

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

2xy + x^2 y' + 2yx y' + y^2 = 0

x^2 y' + 2yx y' = -2xy + y^2

y' = (-2xy + y^2)/(x^2+2yx)

is what i get to

Answer 4

well, i dropped a negative along the way ... - y^2

Answer 5

okay, so I see where I think I went wrong in this equation...yes exactly! Am I supposed to drop that there? Or should we keep it?/

Answer 6

after the implicit run, the rest is just algebra manipulations.

subtracting the nony' parts from left to right, and dividing off the rest; so id keep the negative parts :)

Answer 7

x^2(y) + y^2(x) = -2

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

2xy + x^2 y' + 2yx y' + y^2 = 0

x^2 y' + 2yx y' = -2xy - y^2

y' = (-2xy - y^2)/(x^2+2yx)

Answer 8

okay, so just for confirmation my final answer is the one above??

Answer 9

Or do I need to simplify mroie?

Answer 10

im not sure what the simplest simplified form would be, that is up to whoever is grading it. My teachers tend to be more concerned about showing how i get to a solution instead of some simplification or modification of it into all sorts of identical forms

Answer 11

oh okay, I got you! Thank yo so much for your help, im going to review over this now and compare to my work, I tend to make the smallest mistakes!! Thank you so much!

Answer 12

youre welcome, and yeah ... the calculus parts are simple enough, its the algebra that gets ya most of the time ;)