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

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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Lindsey Gamble
$$\displaystyle{f{{\left({x},{y}\right)}}}={\ln{{\left({x}^{{2}}{y}\right)}}}+{y}^{{3}}{x}^{{2}}$$
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
Thanks, it's helpful because it shows the way. Anyway, there is $$\displaystyle{a}^{{2}}$$ after x at last.