Originally Posted by

**Diego** To make myself clearer I am going to consider the function $\displaystyle f(x) = |x|$. This function can be rewritten as:

$\displaystyle f(x) = \left\{ \begin{matrix}

x & \mbox{ if } 0 \leq x \\

-x & \mbox{ if } 0 > x \

\end{matrix} \right.$

So the derivative is:

$\displaystyle f'(x) = \left\{ \begin{matrix}

1 & \mbox{ if } 0 < x \\

-1 & \mbox{ if } 0 > x \

\end{matrix} \right.$

It can be shown that in x = 0 the derivative does not exist. Apply this idea to your function.