求下列方程所确定的隐函数的导数~~要个详细的过程，麻烦下~~~

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1.两边求导：y'=1+1/2y*y'

(1-1/2y)y'=1

y' =1/(1-1/2y)=2y/(2y-1)

2.两边求导：ln2*2^x+2y'=ln2*2^(x+y)*(1+y')

(2-ln2*2^(x+y)y'=ln2*2^(x+y)-ln2*2^x

y'=(ln2*2^(x+y)-ln2*2^x)/(2-ln2*2^(x+y)

3.两边求导：1=y'+1/(1+y^2)y'

y'=(1+y^2)/(2+y^2)

1) F(x,y)=x+(lny)/2-y

F'x=1,F'y=1/2y-1

dy/dx=-F'x/F'y=-1/(1/2y-1)=2y/(2y-1)

2) F(x,y)=2^x+2y-2^(x+y)

F'x=2^xln2-2^(x+y)ln2=(2^x-2^(x+y))ln2

F'y=2-2^(x+y))ln2

dy/dx=-F'x/F'y=-[(2^x-2^(x+y))ln2]/[2-2^(x+y))ln2]=ln2[2^(x+y)-2^x]/[2-ln2*2^(x+y)]

3) F(x,y)=y+arctany-x

F'x=-1 F'y=1+1/(1+y^2)=(2+y^2)/(1+y^2)

dy/dx=-F'x/F'y=-(1+y^2)/(2+y^2)

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