Page 711 Problem 10

Find \(f_x\), \(f_y\), \(f_{xx}\), \(f_{yy}\), \(f_{xy}\), and \(f_{yx}\) of \(f(x,y)=y^3+3xy^2+3x^2y+x^3\)

Solution

\(f_x=3y^2+6xy+3x^2\)

\(f_y=3y^2+6xy+3x^2\)

\(f_{xx}=6y+6x\)

\(f_{yy}=6y+6x\)

\(f_{xy}=6y+6x\)

\(f_{yx}=6y+6x\)