#### Answer

First Derivative: $w'=\frac{-6}{z^{3}}+\frac{1}{z^{2}}$
Second Derivative: $w''=\frac{18}{z^{4}}-\frac{2}{z^{3}}$

#### Work Step by Step

Using the power rule:
First Derivative:
$w=3z^{-2}-\frac{1}{z}$
$w'=(-2)(3)z^{-2-1}-(-1)z^{-1-1}$
$w'=-6z^{-3}+z^{-2}$
$w'=\frac{-6}{z^{3}}+\frac{1}{z^{2}}$
Second Derivative:
$w'=-6z^{-3}+z^{-2}$
$w''=(-3)(-6)z^{-3-1}+(-2)z^{-2-1}$
$w''=18z^{-4}-2z^{-3}$
$w''=\frac{18}{z^{4}}-\frac{2}{z^{3}}$