What have you tried so far? We need to see your work.
What does the sine function do as its argument gets very large? If you multiply that sine by a quantity (xy) that approaches zero, what happens? Does the definition of f(x,y) at (x^2 + y^2)=0 make it continuous?
What are the partials d/dx and d/dy at points other than (0,0)? Can you say that the limits approaching from below and above 0 are equal?
Lots of questions you could consider, to see if any of them provide insight.
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