Find `(dy)/(dx)` in each of the following: `(x^2+y^2)^2=x y`

Explanation

`(x^{2}+y^{2})^{2}=x y`


`x^{4}+2 x^{2} y^{2}+y^{4}-x y=0`


Differentiating w.r.t `x`,


`4 x^{3}+2[x^{2} 2 y(frac{d y}{d x})+y^{2}(2 x)]+4 y^{3}(frac{d y}{d x})-[frac{x d y}{d x}+y(1)]=0`


`(frac{d y}{d x})[4 x^{2} y+4 y^{3}-x]+4 x^{3}+4 x y^{2}-y=0`


`(frac{d y}{d x})[4 x^{2} y+4 y^{3}-x]=y-4 x^{3}-4 x y^{2}`


`(frac{d y}{d x})=frac{y-4 x^{3}-4 x y^{2}}{4 x^{2} y+4 y^{3}-x}`