Calc2.25

From Exampleproblems

Find the derivative of $y\,$ with respect to $x\,$ : $x+xy+x^2+xy^2=0\,$

You could solve this for $y\,$ as it is a quadratic in $y\,$ but it is probably much nicer to differentiate implicitly.

$1+y+xy'+2x+y^2+2xyy'=0'\,$

Solving this for $y'\,$ gives

$y'=\frac{-(1+y+2x+y^2)}{x+2xy}\,$