# Thread: Need help with derivative problems ):

1. ## Need help with derivative problems ):

...solved!

2. If $f(x) = |x|$, then $f'(x) = \frac{|x|}{x}$.

Therefore, if $f(x) = |x|^\frac{3}{2}$, then $f'(x) = \frac{3}{2}|x|^\frac{1}{2} \times \frac{|x|}{x}$.

$f'(x)$ fails to exist at $x = 0$ (because of division by zero). It exists at all other values of $x$.

Likewise, $f''(x)$ is undefined at $x = 0$ but defined for all other values of $x$.