Question

求多元函数的偏导数或全微分 1、 z=sin(x2y3),求бz/бx,бz/бy 2、 z=f(exy,y2),其中f

Answer 1

(1)бz/бx=cos(x^2*y^3)*2x

бz/бy=cos(x^2*y^3)*3y^2

(2)令g(x)=e^(xy),h(x)=y^2

则dz=f'*g'+f'*h'=f'[(бg/бx)*dx+(бg/бy)*dy]+f'[(бh/бx)*dx+(бh/бy)*dy]

=f'(ye^xydx+xe^xydy)+f'(2ydy)

=f'ye^xydx+f'(xe^xy+2y)dy

不一定对,多年不学高等数学了,但思路应该就是这样.