#### Answer

First Derivative: w' = 21$z^{6}$ - 21$z^{2}$ + 42$z$
Second Derivative: w'' = 126$z^{5}$ - 42$z$ + 42

#### Work Step by Step

Using the Power Rule:
First Derivative:
w = 3$z^{7}$ - 7$z^{3}$ + 21$z^{2}$
w' = (7)(3)$z^{7-1}$ - (3)(7)$z^{3-1}$ + (2)(21)$z^{2-1}$
w' = 21$z^{6}$ - 21$z^{2}$ + 42$z$
Second Derivative:
w' = 21$z^{6}$ - 21$z^{2}$ + 42$z$
w'' = (6)(21)$z^{6-1}$ - (2)(21)$z^{2-1}$ + (1)42$z^{1-1}$
w'' = 126$z^{5}$ - 42$z$ + 42