Question

设z=e^xy(x+y)则对x，对y的偏导数怎么求，答案是什么

设z=e^xy(x+y)则对x，对y的偏导数怎么求，答案是什么

Answer 1

简单计算一下即可，答案如图所示

Answer 2

z=e^xy *(x+y)
那么对x求偏导数得到
Z'x=(e^xy)' *(x+y)+e^xy *(x+y)'
=y *e^xy *(x+y)+e^xy
=e^xy *(xy+y^2+1)
同理Z'y=e^xy *(xy+x^2+1)