Find the partial derivative fxx and fyy of f(x,y) = x2 + x3y2 - y2 + x | Mathematics I 2079

Mathematics I20795 marksNumerical: partial derivativesPartial derivatives

Find the partial derivative $f_{xx}$ and $f_{yy}$ of $f(x,y) = x^2 + x^3y^2 - y^2 + xy$ at $(1,2)$ . [5]

Find the partial derivative $f_{xx}$ and $f_{yy}$ of $f(x,y) = x^2 + x^3y^2 - y^2 + xy$ at $(1,2)$. [5]

Function: $f(x,y) = x^2 + x^3y^2 - y^2 + xy$ - Evaluation point: $(x, y) = (1, 2)$ - Required: $f{xx}$ and $f{yy}$ at $(1,2)$ All data is present. --- Treat $y$ as constant: $fx = 2x + 3x^2y^2 + y$ $f{xx} = \frac{\partial}{\partial x}\left(2x + 3x^2y^2 + y\right) = 2 + 6xy^2$ Evaluate at

Function: $f(x,y) = x^2 + x^3y^2 - y^2 + xy$ - Evaluation point: $(x, y) = (1, 2)$ - Required: $f{xx}$ and $f{yy}$ at $(1,2)$ All data is present. --- Treat $y$ as constant: $$fx = 2x + 3x^2y^2 + y$$ $$f{xx} = \frac{\partial}{\partial x}\left(2x + 3x^2y^2 + y\right) = 2 + 6xy^2$$ Evaluate at

Find the partial derivative fxx and fyy of f(x,y) = x2 + x3y2 - y2 + xy at (1,2).