设u=f(x+y,x-y)具有二阶连续偏导数,求u对X的连续二次偏导数答:= f1(x+y,x-y)*1+f2(x+y,x-y)*1 = f1(x+y,x-y)+f2(x+y,x-y),D(Du/Dx)/Dx = (D/Dx)[f1(x+y,x-y)+f2(x+y,x-y)]= [f11(x+y,x-y)+f12(x+y,x-y)]+[f21(x+y,x-y)+f22(x+y,x-y)]= [f11(x+y,x-y)+2*f12(x+y,x-y)]+f22(x+y,x-y)...
隐函数的二阶偏导 设方程F(x,yz)=0确定隐函数z=z(x,y),求z对x的二阶...答:F(x,yz)=0 求导:(用ez/ex表示z对x的偏导数)F1'(x,yz)+F2'(x,yz)*y*ez/ex=0 解得:ez/ex=-F1'(x,yz)/y*F2'(x,yz)则 e^2z/ex^2 ={[-F11''(x,yz)-y*ez/ex*F12''(x,yz)]*y*F2'(x,yz)-y*F1'(x,yz)*[F21'(x,yz)+yF22'(x,yz)*ez...