Consider this multivariable function. f(x,y)=ye^(3x)+y^2 a) Find f_y(x,y) b) What is value of f_(xx)(0,3)?

Consider this multivariable function. f(x,y)=ye^(3x)+y^2 a) Find f_y(x,y) b) What is value of f_(xx)(0,3)?

Multivariable functions
asked 2020-11-20
Consider this multivariable function. \(\displaystyle{f{{\left({x},{y}\right)}}}={y}{e}^{{{3}{x}}}+{y}^{{2}}\)
a) Find \(\displaystyle{{f}_{{y}}{\left({x},{y}\right)}}\)
b) What is value of \(\displaystyle{{f}_{{\times}}{\left({0},{3}\right)}}\)?

Answers (1)

a) \(\displaystyle{{f}_{{y}}{\left({x},{y}\right)}}=\frac{{\partial{f}}}{{\partial{y}}}=\frac{\partial}{{\partial{y}}}{\left[{y}{e}^{{{3}{x}}}+{y}^{{2}}\right]}\)
b) \(\displaystyle\frac{{\partial{f}}}{{\partial{x}}}={f}_{{x}}=\frac{\partial}{{\partial{x}}}{\left[{y}{e}^{{{3}{x}}}+{y}^{{2}}\right]}\)

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