Question

use implicit differentiation to solve: y^2-xy+x^2=2

Answer 1

y'=(2-2x+y)/(2y-x) I did this fast so, you might want to check it.

Answer 2

you want to differentiate both sides

Answer 3

y is a function of x, so dy/dx will follow the chain rule

Answer 4

thus y^2 becomes

2y*y'

Answer 5

x^2 is explicitly expressed as a function of x,
so there is no need to do chain rule for this one

so x^2 just becomes 2x

Answer 6

xy will follow the product rule because it is x times a function of x

so it is like saying x*sin(x)

you will do the product rule for xy and chain rule for y'

Answer 7

so it becomes y + xy'

Answer 8

all you do is to solve for y' from there :)