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F(x,y)=x^3y^3sin(1/(xy)),xy≠0. F(x,y)=0,xy=0. 1.xy=0,显然有 Fx'(x,y)=Fy'(x,y)=0. 2.xy≠0, Fx'(x,y)=3x^2y^3sin(1/(xy))-xy^2cos(1/(xy)), Fy'(x,y)=3x^3y^2sin(1/(xy))-x^2ycos(1/(xy)). 3. xy=0,显然有 Fxy''(x,y)=Fyx''(x,y)=0. 4. xy≠0, Fxy''(x,y)=Fyx''(x,y)= =9x^2y^2sin(1/(xy))-5xycos(1/(xy))-sin(1/(xy)). |
