Question

设f(x,y)具有一阶连续偏导数,z=xf(x^y,e^xy),求dz

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