Just wanted to see if I'm doing this correctly:

Find $\displaystyle f''(x)=|x|^3$

So $\displaystyle f'(x)=(3|x|^2)\frac{x}{|x|}$

$\displaystyle =3|x|x$

$\displaystyle f''(x)=3|x|\frac{d}{dx}x+3\frac{d}{dx}|x|x$

$\displaystyle =3|x|+3\frac{x}{|x|}x$

$\displaystyle =3|x|+\frac{3x^2}{|x|}$

Does that seem right?