Question

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

Derivatives
ANSWERED
asked 2021-02-20
Find the partial derivatives, \(\displaystyle{f}_{{{x}}}\ {\quad\text{and}\quad}\ {f}_{{{y}}},\ {f}{\quad\text{or}\quad}\ {f{{\left({x},{y}\right)}}}={\left({e}^{{{x}}}\right)}^{{{2}{y}}}\)

Answers (1)

2021-02-22
Step 1
The given function is \(\displaystyle{f{{\left({x},{y}\right)}}}={\left({e}^{{{x}}}\right)}^{{{2}{y}}}\)
Step 2
Obtain the partial derivative as follows.
\(\displaystyle{f}_{{{x}}}'={e}^{{{2}{x}{y}}}\cdot{2}{y}\)
\(\displaystyle{f}_{{{y}}}'={e}^{{{2}{x}{y}}}\cdot{2}{x}\)
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