Question

Calculate the derivative of y with respect to x.
x2 y + 2 x y2 = x + y

Answer 1

and those are squared exp

Answer 2

X^2 + 4xy = x

Answer 3

\[x^2 y + 2 x y^2 = x + y\]implicit right?

Answer 4

Yep it is implicits

Answer 5

differentiate implicitly with product and chain rules:\[2xy+x^2y'+4xyy'+2y^2=1+y'\]collect our y's on one side:\\[2xy+2y^2-1=y'-x^2y'-4xyy'=y'(1-x^2-4xy)\]solve for y'\[y'={2xy+2y^2-1\over1-x^2-4xy}\]