# Need help with derivative problems ):

• October 18th 2010, 08:58 AM
swtbellrose
Need help with derivative problems ):
...solved!
• October 18th 2010, 09:28 AM
NOX Andrew
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 $x$.