关于数学微积分的设u=Xyz,则du=题目中yz是上标的

Question

关于数学微积分的
设u=Xyz ,则du=_____
题目中yz是上标的

Answer 1

u=xyz
Ux=yz
Uy=xz
Uz=xy
所以:
du=(yz)dx+(xz)dy+(xy)dz
U=x^(yz)
Ux=(yz)x^(yz-1)
Uy=(x^z)^y*ln(x^z)
Uz=(x^y)^z*ln(x^y)
du=[(yz)x^(yz-1)]dx+[z(x^z)^y*ln(x)]dy+[y*(x^y)^z*ln(x)]dz