Find the derivative of the inverse function of: $$ f(x)=\frac{1}2\sin(2x) + x $$
I already know that this function is one-to-one.
What I've done:
$$ y=\frac{1}2\sin(2x) + x $$
$$ 2y - 2x = \sin(2x) $$
$$ \frac{\arcsin(2y - 2x)}2 = x $$
Is this a suitable way to do it, and how do I eleminate the x that is left inside arcsin?