Find $g^{\text{'}}(x)$ for the given function. Then find $g^{\text{'}}(-2),g^{\text{'}}(0),$ and $g^{\text{'}}(2).$

$g(x)=\sqrt[\phantom{2}]{3x}$

Find $g^{\text{'}}(x)$ for the given function.

$g^{\text{'}}(x)=$

$$

Find $g^{\text{'}}(-2).$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.g^{\text{'}}(-2)=($Type an exact answer.$)$

B$.$ The derivative does not exist.

Find $g^{\text{'}}(0).$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.g^{\text{'}}(0)=($Type an exact answer.$)$

B$.$ The derivative does not exist.

Find $g^{\text{'}}(2).$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.g^{\text{'}}(2)=($Type an exact answer.$)$

B$.$ The derivative does not exist.