Question

x＋2y＋z＝e的z次幂求x y偏导数怎么求

Answer 1

偏导P

1+2dy/dx+Pz/Px=e^z *Pz/Px

Pz/Px=(1+2dy/dx) / (e^z-1)

同理Pz/Py=(dx/dy+2) / (e^z-1)

若求dz

dz=Pz/Pxdx+Pz/Pydy

=(dx+2dy) / (e^z-1) +(dx+2dy)/(e^z-1)

=3/(e^z-1) (dx+dy)