Question

Question #ac40e

Answer 1

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

Explanation:

`x^2+y^2=xy`

After taking derivative both sides,

`2x+2y*y'=y+xy'`

`2x-y=(x-2y)*y'`

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

Answer 2

`x^2+y^2=xy`

differentiating with respect to `x`,

`dx^2/dx+dy^2/dx=(d(xy))/dx`

applying product rule for the derivative of `xy`

`2x + 2y dy/dx = dx/dx*y + dy/dx*x`

`2x + 2y dy/dx = y + xdy/dx`

`2x -y = xdy/dx-2y dy/dx`

`2x -y = (x-2y) dy/dx`

`dy/dx=(2x -y)/ (x-2y)`

-Sahar