设函数z=f(u,v)具有二阶连续偏导数,试求函数z=f(x,yx)对x的二阶偏导数...答:z=f(x,yx)dz/dx=f1'(x,yx)+f2'(x,yx)*y d^2z/dx^2=f11''(x,yx)+f12''(x,yx)*y+yf21''(x,yx)+yf22''(x,yx)*y =f11''(x,yx)+(y+1)*f12''(x,yx)+y^2*f22''(x,yx)
设二阶偏导数连续的函数z=f(u,v),u=xy,v=x^2-y^2,求δz/δx,δz/...答:z=f(u,v),u=xy,v=x^2-y^2 du/dx=y,du/dy=x dv/dx=2x,dv/dy=-2y dz/dx=dz/du*du/dx+dz/dv*dv/dx =df/du*y+df/dv*2x dz/dy=dz/du*du/dy+dz/dv*dv/dy =df/du*x-df/dv*2y