Since xy=0 at point (0, y), the derivative formula cannot be used, and it should be calculated according to the definition of partial derivative. Partial derivative of x at (0, y) =lim[f(x, y)-f(0, y)]/x(x tends to 0) = lim [xarctan (y/x)- According to the fact that the product of infinitesimal and bounded quantity is infinitesimal, we know that limxarctan(y/x)=0, so