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.
z对x的偏导数 z'(x)=cos(xy)*y+2cos(xy)[-sin(xy)*y] =ycos(xy)[1-2sin(xy)]. z'(y)=cos(xy)*x+2cos(xy)[-sin(xy)*x] =xcos(xy)[1-2sin(xy)].[
z＝sin(xy)＋[cos(xy)]^2 z在对x的偏导数是：cos(xy)×y＋2×cos(xy)×[－sin(xy)]×y＝y×[cos(xy)－sin(2xy)]。 z对y的偏导数是：y×[cos(xy)－sin(2xy)]。
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