Chapter 7 - Ingredients of Multivariable Change: Models, Graphs, Rates - 7.3 Activities - Page 558: 14

\begin{align*} (a)&\ g_x=6.4 x y z^{2}+2.9y x^{y-1}\\ (b)&\ g_y = 3.2 x^{2} z^{2}+2.9 x^{y}\ln (x)+z\\ (c)&\ g_z= 6.4 x^{2} y z+1\\ \end{align*}

Given $$g(x, y, z)=3.2 x^{2} y z^{2}+2.9 x^{y}+z$$ Since \begin{align*} (a)&\ g_x=6.4 x y z^{2}+2.9y x^{y-1}\\ (b)&\ g_y = 3.2 x^{2} z^{2}+2.9 x^{y}\ln (x)+z\\ (c)&\ g_z= 6.4 x^{2} y z+1\\ \end{align*}