Question

求“u=x的yz次方”的全微分

Answer 1

先求出三个偏导数，
ux=yz·x^(yz-1)
uy=x^(yz)·lnx·z
uz=x^(yz)·lnx·y
∴全微分为
du=ux·dx+uy·dy+uz·dz
=x^(yz)[yz/x·dx+lnx·z·dy+lnx·y·dz]

Answer 2

u = x^(yz)

au/ax=yzx^(yz-1)

au/ay=zln(x)x^(yz)

au/az=yln(x)x^(yz)

du = au/axdx + au/aydy + au/azdz=yzx^(yz-1)dx+zln(x)x^(yz)dy+yln(x)x^(yz)dz