设（xy）^z=e,则z对x的偏导

Question

如题所述

Answer 1

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