Derivative question.

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August 14th 2011, 09:51 PM
rushton

Derivative question.

Is this right?

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

So

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

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

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

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

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

though and there are a few different answers....none of them mine.
August 14th 2011, 09:56 PM
pickslides

Re: Derivative question.

Heres some working of the problem

derive cos^(-1)(cos(x)) - Wolfram|Alpha
August 14th 2011, 10:15 PM
rushton

Re: Derivative question.

Ok I see where I went wrong in my my substitution working.

So

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

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