z=arctan(y/x)那么∂z/∂x=1/(1+y²/x²) *∂(y/x)/∂x=x²/(x²+y²) *(-y/x²)= -y/(x²+y²)再继续对y 求偏导，得到∂²z/∂x∂y=[-(x²+y²)+y*2y]/(x²+y²)²=(y²-x²)/(x²+y²)²
