Question

find dy/dx by implicit differentiation: xy+x+y=(x^2)(y^2)

Answer 1

(x)(y')+(y)(1)+1+y'=(x^2)(2yy')+(y^2)(2x)
//Simplify.

Answer 2

how do i simplify that

Answer 3

Take the total derivative of\[x+y+x y=x^2 y^2\]\[y dx+x dy+dx+dy=2 x^2 y dy+2 x y^2 dx \]solve for dy\[dy=\frac{-2 x y^2 dx+y dx+dx}{2 x^2 y-x-1} \]and then divide both sides by dx\[\frac{dy}{dx}=-\frac{-2 x y^2+y+1}{-2 x^2 y+x+1} \]