xy-e^x+e^y=0,求dy/dx|x=0?
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xy-e^x+e^y=0,求dy/dx|x=0?xy-e^x+e^y=0,求dy/dx|x=0?xy-e^x+e^y=0,求dy/dx|x=0?将xy-e^x+e^y=0两边取导得:ydx+xdy-e
xy-e^x+e^y=0,求dy/dx|x=0?
xy-e^x+e^y=0,求dy/dx|x=0?
xy-e^x+e^y=0,求dy/dx|x=0?
将xy-e^x+e^y=0两边取导得:
ydx+xdy-e^xdx+e^ydy=0
解得:dy/dx=﹙y--e^x﹚/﹙x-+e^y﹚
当x=0时,∴e^y=1,y=0
∴dy/dx|x=0=(0-1)/﹙0+1﹚=-1
y+xy`-e^x+y`e^y=0
xy-e^x+e^y=0
x=0
0-1+e^y=0
y=0
0+0y`-e^0+y`e^0=0
-1+y`=0
dy/dx=1
xy-e^x+e^y=0 (1)
求dy/dx x=0时。
由(1)代入x=0,
e^[y(0)] = 1,
即 y(0) = 0 (2)
对(1)式两边对x求导,
y+xy'-e^x+y'e^y=0
y'(x+e^y)=-y+e...
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xy-e^x+e^y=0 (1)
求dy/dx x=0时。
由(1)代入x=0,
e^[y(0)] = 1,
即 y(0) = 0 (2)
对(1)式两边对x求导,
y+xy'-e^x+y'e^y=0
y'(x+e^y)=-y+e^x
y'=(e^x-y)/(e^y+x) (3)
令x=0, 由(2)、(3)得到:
y'(0)=[1-y(0)] / [e^y(0)]
y'(0)= 1 。
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