分类：教育/科学-理工学科-数学
问题：高等数学的一道计算题求函数z=sin(xy)+cos平方（xy) 
求z=sin(xy)+cos平方（xy)的偏导数
回答：z=sin(xy)+cos²(xy)
эz/эx=[cos(xy)]y-2[cos(xy)sin(xy)y=ycos(xy)-ysin(2xy).
эz/эy=[cos(xy)]x-2[cos(xy)sin(xy)]x=xcos(xy)-xsin(2xy).
э²z/эxэy=cos(xy)-y[sin(xy)]x-sin(2xy)-y[cos(2xy)]2x
=cos(xy)-xysin(xy)-sin(2xy)-2xycos(2xy)
э²z/эyэx=cos(xy)-x[sin(xy)]y-sin(2xy)-x[cos(2xy)]2y
=c0s(xy)-xysin(xy)-sin(2xy)-2xycos(2xy)=э²z/эxэy.