Question

# Write formulas for the indicated partial derivatives for the multivariable function. g(x,y,z)=3.1x^2yz^2+2.7x^y+z a)g_x b)g_y c)g_z

Multivariable functions
Write formulas for the indicated partial derivatives for the multivariable function. $$\displaystyle{g{{\left({x},{y},{z}\right)}}}={3.1}{x}^{{2}}{y}{z}^{{2}}+{2.7}{x}^{{y}}+{z}$$
a)$$\displaystyle{g}_{{x}}$$
b)$$\displaystyle{g}_{{y}}$$
c)$$\displaystyle{g}_{{z}}$$

2021-02-23
a) $$\displaystyle\frac{{\partial{g}}}{{\partial{x}}}=\frac{\partial}{{\partial{x}}}{\left[{3.1}{x}^{{2}}{y}{z}^{{2}}+{2.7}{x}^{{y}}+{z}\right]}$$
$$\displaystyle\frac{{\partial{g}}}{{\partial{x}}}={\left({3.1}\right)}\cdot{2}{x}{y}{z}^{{2}}+{2.7}{y}{x}^{{{y}-{1}}}+{0}$$
$$\displaystyle\frac{{\partial{g}}}{{\partial{x}}}={6}\cdot{2}{x}{y}{z}^{{2}}+{2.7}{y}{x}^{{{y}-{1}}}$$
b) $$\displaystyle\frac{{\partial{g}}}{{\partial{y}}}=\frac{\partial}{{\partial{y}}}{\left[{3.1}{x}^{{2}}{y}{z}^{{2}}+{2.7}{x}^{{y}}+{z}\right]}$$
$$\displaystyle\frac{{\partial{g}}}{{\partial{y}}}={3.1}{x}^{{2}}{z}^{{2}}+{2.7}{x}^{{y}}{\ln{{\left({x}\right)}}}+{0}$$
$$\displaystyle\frac{{\partial{g}}}{{\partial{y}}}={3.1}{x}^{{2}}{z}^{{2}}+{2.7}{x}^{{y}}{\ln{{\left({x}\right)}}}$$
c)$$\displaystyle\frac{{\partial{g}}}{{\partial{z}}}=\frac{\partial}{{\partial{z}}}{\left[{3.1}{x}^{{2}}{y}{z}^{{2}}+{2.7}{x}^{{y}}+{z}\right]}$$
$$\displaystyle\frac{{\partial{g}}}{{\partial{z}}}={3.1}{x}^{{2}}{y}{x}{\left({2}{z}\right)}+{0}+{1}$$
$$\displaystyle\frac{{\partial{g}}}{{\partial{z}}}={6}\cdot{2}{x}^{{2}}{y}{z}+{1}$$