设f(x,y)具有一阶连续偏导数,z=xf(x^y,e^xy),求dz
问题描述：
设f(x,y)具有一阶连续偏导数,z=xf(x^y,e^xy),求dz
答
根据一阶全微分形式不变得dz=d(xf(x^y,e^xy)=f(x^y,e^xy)dx+xd(f(x^y,e^xy))=f(x^y,e^xy)dx+x[f1'd(x^y)+f2'(de^xy)]= f(x^y,e^xy)dx+x{f1'[(y-1)x^(y-1)dx+x^ylnydy]+f2'(ye^xydx+xe^xydy)}自己整理OK...