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1.f(x,y)=ln(x+x/y)
fx=(1+1/y)/(x+x/y) = 1/x;
fy=(-x/y^2)/(x+x/y) = -1/(y^2+y)
fx(1,1) =1,fy(1,1)=-1/2
f(x,y)在P0(1,1)处的偏导数连续
f(x,y)在P0(1,1)处可微(可微的充分条件)
全微分:fx*△x+fy*△y = △x-(1/2)△y.
2.u=e^(xy)
ux=[e^(xy)]' *(xy)' = y*e^(xy)
uxy=(ux)y= [y*e^(xy)]' = e^(xy) + y* x*e^(xy)
=(x*y+1)*e^(xy)
对x求偏导,将y看做常数;同样对y求偏导,将x看做常数
fx=(1+1/y)/(x+x/y) = 1/x;
fy=(-x/y^2)/(x+x/y) = -1/(y^2+y)
fx(1,1) =1,fy(1,1)=-1/2
f(x,y)在P0(1,1)处的偏导数连续
f(x,y)在P0(1,1)处可微(可微的充分条件)
全微分:fx*△x+fy*△y = △x-(1/2)△y.
2.u=e^(xy)
ux=[e^(xy)]' *(xy)' = y*e^(xy)
uxy=(ux)y= [y*e^(xy)]' = e^(xy) + y* x*e^(xy)
=(x*y+1)*e^(xy)
对x求偏导,将y看做常数;同样对y求偏导,将x看做常数
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