1. ## Find this derivative

Hi guys.

Find the derivative of this function:

$|(x)/(1-x^2)|$

Thanks.

2. Let $u = x^2 \implies du = 2x dx \imples dx = \dfrac{du}{2x}$

$\dfrac{x du}{2x(1-u)} = \dfrac{1}{2} \cdot \dfrac{1}{1-u}$

You'll still need to use the chain rule on that -u of course

3. The function is:

$f(x)=\begin{Bmatrix} \dfrac{x}{1-x^2} & \mbox{ if }& x\in (-\infty,-1)\cup [0,1)\\{}\\\dfrac{x}{x^2-1} & \mbox{if}& x\in (-1,0)\cup (1,+\infty)\end{matrix}$

Fernando Revilla

4. You can also use the chain rule together with the fact that the derivative of $|x|$ is $\frac{x}{|x|}$.

5. Notice that |x| does NOT have a derivative at x= 0. The given function also does not exist at x= 1 and x= -1 and so does not have a derivative at x=-1, x= 0, and x= 1.