Chapter 3 - Section 3.3 - Differentiation Rules - Exercises - Page 136: 51

$w' = 6(ze^{2z}+z^{2}e^{2z})=6ze^{2z}(1+z)$ $w'' = 6e^{2z}(1+4z+2z^{2})$

$w = 3z^{2}e^{2z}$ $w' = 3(2ze^{2z}+2z^{2}e^{2z})$ $w' = 6(ze^{2z}+z^{2}e^{2z})$ $w'' = 6(e^{2z}+2ze^{2z} + 2ze^{2z}+2z^{2}e^{2z})$ $w'' = 6(e^{2z}+4ze^{2z} +2z^{2}e^{2z})$ $w'' = 6e^{2z}(1+4z+2z^{2})$