Question

# Find the partial derivatives, f_{x}\ and\ f_{y},\ for\ f(x, y) = (e^{x})^{2y}

Derivatives
Find the partial derivatives, $$\displaystyle{f}_{{{x}}}\ {\quad\text{and}\quad}\ {f}_{{{y}}},\ {f}{\quad\text{or}\quad}\ {f{{\left({x},{y}\right)}}}={\left({e}^{{{x}}}\right)}^{{{2}{y}}}$$

The given function is $$\displaystyle{f{{\left({x},{y}\right)}}}={\left({e}^{{{x}}}\right)}^{{{2}{y}}}$$
$$\displaystyle{f}_{{{x}}}'={e}^{{{2}{x}{y}}}\cdot{2}{y}$$
$$\displaystyle{f}_{{{y}}}'={e}^{{{2}{x}{y}}}\cdot{2}{x}$$