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- Oct 18th 2010, 08:58 AMswtbellroseNeed help with derivative problems ):
...solved!

- Oct 18th 2010, 09:28 AMNOX Andrew
If $\displaystyle f(x) = |x|$, then $\displaystyle f'(x) = \frac{|x|}{x}$.

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

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

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