1. ## Chain rule?

Ok, so in an equation I have the following:
$\displaystyle y^2$

If I want to find the derivative of this, I figured I should use the chain rule on this one:
$\displaystyle \frac{dy}{dy} \cdot \frac{dy}{dx}=1 \frac{dy}{dx}$

But is that correct? I don't get it if it's wrong. :/

2. The answer you got is almost right. It should be:
$\displaystyle 2y\frac{dy}{dx}$
I'm going to name this equation as follows
$\displaystyle f = y^2$
I'm using f instead of the traditional y so the equation makes sense

The chain rule states $\displaystyle \frac{dy}{dx} = \frac{dy}{du} * \frac{du}{dx}$

In your case where $\displaystyle u = y$
$\displaystyle f = u^2$
$\displaystyle \frac{df}{du} = 2u$

Then when:
$\displaystyle u = y$
$\displaystyle \frac{du}{dx} = \frac{dy}{dx}$

So using the chain rule in this case you get:
$\displaystyle \frac{df}{dx} = \frac{df}{du} * \frac {du}{dx}$
$\displaystyle \frac{df}{dx} = 2u * \frac{dy}{dx}$
Substituting y back in it becomes:
$\displaystyle 2y\frac{dy}{dx}$

You had the right idea and almost got it correct. The chain rule can be easy to mess up especially when y is involved.