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- #1

I did some of the problem on MatLab but I'm having a difficult time evaluating the derivatives at (0,0). Also, MatLab gave me the same answer for f

_{xy}and f

_{yx}, which according to the problem isn't correct. Any ideas?

I used MatLab and computed:

f

_{x}(x,y)=(2*x^2*y)/(x^2 + y^2) + (y*(x^2 - y^2))/(x^2 + y^2) - (2*x^2*y*(x^2 - y^2))/(x^2 + y^2)^2

and

f

_{y}(x,y)=(x*(x^2 - y^2))/(x^2 + y^2) - (2*x*y^2)/(x^2 + y^2) - (2*x*y^2*(x^2 - y^2))/(x^2 + y^2)^2

I also used MatLab to compute f

_{xy}and f

_{yx}, both gave me the same answer:

(x^2 - y^2)/(x^2 + y^2) + (2*x^2)/(x^2 + y^2) - (2*y^2)/(x^2 + y^2) - (2*x^2*(x^2 - y^2))/(x^2 + y^2)^2 - (2*y^2*(x^2 - y^2))/(x^2 + y^2)^2 + (8*x^2*y^2*(x^2 - y^2))/(x^2 + y^2)^3