Is this right?

$\displaystyle y=cos^{-1}(cos(x))$

So

$\displaystyle \frac{dy}{dx}cos^{-1}(cos (x))=1$

I figure this as (I'm not sure if my working here is flawed or not)

$\displaystyle \begin{align*} y&=cos^{-1}(cos(x))\\cos( y)&=cos(x)\\y&=x \end{align*}$

And I also did it via substitution and got the same answer. I googled

$\displaystyle \frac{d}{dx}cos^{-1}(cos (x))$

though and there are a few different answers....none of them mine.