If `(x^2+y^2)^2=x y` , find `(dy)/(dx)`

Answer

N/a

Explanation

We have, `(x^(2)+y^(2))^(2) = xy`
On differentiating both sides w.r.t. x, we get
`(d)/(dx) (x^(2)+y^(2))^(2) = d/(dx) (xy)`
`rArr 2(x^(2)+y^(2)).(d)/(dx) (x^(2)+y^(2)) = x.(d)/(dx) +y.(d)/(dx) x`
`rArr 2(x^(2)+y^(2)).(2x+2y'(dy)/(dx))=x'(dy)/(dx)+y`
`rArr 2x^(2).2x+2x^(2).2y'(dy)/(dx)+2y^(2).2x+2y^(2).2y'(dy)/(dx)=x'(dy)/(dx)+y`
`rArr (dy)/(dx) [4x^(2)y+44y^(3)-x]=y-4x^(3)-4xy^(2)`
`:. (dy)/(dx) = ((y-4x^(3)-4xy^(2)))/((4x^(2)y+4y^(3)-x))`