求二阶偏导函数z=arctan(xy)?
求二阶偏导函数z=arctan(xy)
令u=y/x; dz/dx=dz/du*du/dx;dz/dy=dz/du*du/dy; dz/du=1/(1+u^2)=x^2/(x^2+y^2),du/dx=-y/x^2,du/dy=1/x; 所以 dz/dx=-y/(x^2+y^2), dz/dy=x/(x^2+y^2); d(dz/dx)/dx=-y/(x^2+y^2)^2*2*x=-2xy/(x^2+y^2)^2; d(dz/dy)/dy=x/(x^2+y^2)^2*2*y=2xy/(x^2+y^2);
答:令u=y/x; dz/dx=dz/du*du/dx;dz/dy=dz/du*du/dy; dz/du=1/(1+u^2)=x^2/(x^2+y^2),du/dx...详情>>
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