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求Z的全微分：Z=arcsin（xy）Z=xsin(x+y)
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求Z的全微分：Z=arcsin（xy） Z=xsin(x+y)
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答案和解析
Z=arcsin(xy)
Z'xy=1/√(1-(xy)^2)
(xy)'x=y
(xy)'y=x
dZ= Z'xy *(xy)'x dx+Z'xy*(xy)'y dy
=ydx/√(1-(xy)^2 +xdy/√(1-(xy)^2
Z=xsin(x+y)
Z'x=sin(x+y)+xcos(x+y)
Z'y=xcos(x+y)
dZ=Z'x*dx +Z'y*dy
=(sin(x+y)+xcos(x+y)) *dx +xcos(x+y) *dy
Z'xy=1/√(1-(xy)^2)
(xy)'x=y
(xy)'y=x
dZ= Z'xy *(xy)'x dx+Z'xy*(xy)'y dy
=ydx/√(1-(xy)^2 +xdy/√(1-(xy)^2
Z=xsin(x+y)
Z'x=sin(x+y)+xcos(x+y)
Z'y=xcos(x+y)
dZ=Z'x*dx +Z'y*dy
=(sin(x+y)+xcos(x+y)) *dx +xcos(x+y) *dy
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