Transformation to a uniformly rotating frame

Question

I'm midway through a problem at the beginning of a GR course, my question is simply this:

If
$$ x=x'\cos\Omega t-y'\sin\Omega t $$ where $x'$ and $y'$ indicate the rotated frame of reference. What does that make $dx^2$?

I need this so I can make substitutions into the equation: $$ ds^2=c^2dt^2-dx^2-dy^2-dz^2 $$

Answer 1

$$ dx = \cos (\Omega t) dx' -x' \Omega \sin (\Omega t) dt - \sin (\Omega t) dy' -y' \Omega \cos (\Omega t) dt$$

It's basically just the product rule and the chain rule.