Question

(x^2+y^2)^2=xy ,dy/dx=?

Answer 1

solution

(x²+y²)²=xy

then the dy/dx

2(x²+y²)*2x+2ydy/dx=xdy/dx+y

⇒(2x²+2y²)(2x+2ydy/dx)=xdy/dx+y

⇒4x³+4x²ydy/dx+4y²x+4y³dy/dx=xdy/dx+y

⇒ 4x³+4y²x-y=dy/dx(x-4x²y-4y²)

⇒ dy/dx = (4x³+4y²x-y)/(x-4x²y-4y²)