This is stumping me. Find the derivative of the following function:

$\displaystyle

y = \cos ^{ - 1} \left( {\frac{x}

{2}} \right)

$

We know this rule:

$\displaystyle

\frac{d}

{{dx}}\cos ^{ - 1} u = \frac{{ - du/dx}}

{{\sqrt {1 - u^2 } }},|u| < 1

$

So.....

$\displaystyle

\begin{gathered}

u = \tfrac{x}

{2} \hfill \\

\tfrac{{du}}

{{dx}} = \tfrac{1}

{2} \hfill \\

\frac{d}

{{dx}}\cos ^{ - 1} u = \frac{{ - 1/2}}

{{\sqrt {1 - \tfrac{{x^2 }}

{4}} }} = \frac{{ - 1/2}}

{{\sqrt {4 - x^2 } }} \hfill \\

\end{gathered}

$

But this is wrong....it should be....

$\displaystyle

y = \cos ^{ - 1} \left( {\frac{x}

{2}} \right) = \frac{{ - 1}}

{{\sqrt {4 - x^2 } }}

$

What's going on here?