How to find expressions for f_{x x} and f_{y y}

Teddy Dillard 2022-01-04 Answered
How to find expressions for \(\displaystyle{f}_{{{x}{x}}}\) and \(\displaystyle{f}_{{{y}{y}}}\) for the multivariable function \(\displaystyle{f{{\left({x},{y}\right)}}}={\ln{{\left({x}^{{2}}{y}\right)}}}+{y}^{{3}}{x}^{{2}}\)?

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Expert Answer

Lindsey Gamble
Answered 2022-01-05 Author has 4878 answers
\(\displaystyle{f{{\left({x},{y}\right)}}}={\ln{{\left({x}^{{2}}{y}\right)}}}+{y}^{{3}}{x}^{{2}}\)
For finding \(\displaystyle{f}_{{x}}\), we have to differentiate \(\displaystyle{f{{\left({x},{y}\right)}}}\) with respect to x as follows:
\(\displaystyle{f}_{{x}}={\frac{{{2}{x}{y}}}{{{x}^{{2}}{y}}}}+{y}^{{3}}\)
Now, for finding \(\displaystyle{f}_{{{x}{x}}}\), differentiate \(\displaystyle{f}_{{x}}\) with respect to \(\displaystyle{x}\).
Try in the same way for \(\displaystyle{f}_{{{y}{y}}}\).
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raefx88y
Answered 2022-01-06 Author has 2271 answers
Thanks, it's helpful because it shows the way. Anyway, there is \(\displaystyle{a}^{{2}}\) after x at last.
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