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?