Basically, I am trying to find the implicit derivative for this problem, but I am stuck after a few steps.
$$x^2y^2=x+y$$
I have calculated the derivatives of each term and used the product rule to combine everything, which has gotten me to this step.
$$(x^2)\left(2y\frac{dy}{dx}\right)+(y^2)(2x)=1+\frac{dy}{dx}$$
However, after reaching this step, I am stuck. I have tried isolating the terms but when I do so, something does not look right, and this confuses me as there are $2 dy/dx$'s. How can I solve this problem? Any help is appreciated. Thanks.
Bring all terms with $dy/dx$ to one side,$$2xy^2-1=\frac{dy}{dx}[1-2x^2y]$$Now divide both sides by $1-2x^2y$ to get$$\frac{dy}{dx}=\frac{2xy^2-1}{1-2x^2y}$$