
Derivative question.
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.

Re: Derivative question.

Re: Derivative question.
Ok I see where I went wrong in my my substitution working.
So
$\displaystyle \frac{dy}{dx}cos^{1}(cos(x))=\frac{sin(x)}{sin(x)}$