设函数f(u,v)具有两阶连续偏导数z=f(x^y ,y^x), 求dz
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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f(u,v)为二元可微函数,z=f(x^y,y^x),求∂z/∂x,∂z/∂y答：z = f(x^y, y^x)，记 u = x^y, v = y^x，则 ∂u/∂x = yx^(y-1), ∂u/∂y = x^ylnx, ∂v/∂x = y^xlny, ∂v/∂y = xy^(x-1).∂z/∂x = (∂f/∂u)(∂u/∂...
Z=f(u,x,y),u=xe^y,其中f具有二阶连续偏导数,求Z〃xx答：δz/δx=f1(u,x,y)e^y+f2(u,x,y),δz/δy=f1(u,x,y)xe^y+f3(u,x,y),δ^2z/δx^2=[f11(u,x,y)e^y+f12(u,x,y)]e^y+ +f12(u,x,y)e^y+f22(u,x,y),δ^2z/δxδy=[f11(u,x,y)xe^y+f13(u,x,y)]e^y+f1(u,x,y)e^y +f12(u,x,y)xe^y+f2...
