z=(e^u)sinv,u=xy^2,v=x-y,求dz

题目

z=(e^u)sinv,u=xy^2,v=x-y,求dz

答案

dz=(e^u)sinvdu+(e^u)cosvdv
=(e^u)sinv[y²dx+2xydy]+(e^u)cosv[dx-dy]
=e^(xy²)[y²sin(x-y)+cos(x-y)]dx+e^(xy²)[2xysin(x-y)-cos(x-y)]dy