Deriving 4x^3 + ln y^2 + 2y = 2x
I think the first step is; 12x^2 + 1 / y^2 + and here is where I'm stuck. What is the derivative of the 2y and 2x?
You have to use implicit differentiation. This should be easy, I think it is the $\displaystyle ln(y^2)$ term that is confusing you.
One of the properties of logarithms allows you to write:
$\displaystyle ln(y^2)=2ln(y)$
Use the chain rule to differentiation this:
$\displaystyle 2\frac{d}{dx}ln(y)=\frac{2}{y}\frac{dy}{dx}$
That should help.