高等数学隐函数题高等数学题.跪求第一大题所有小题的过程.悬赏酌情考虑.
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高等数学隐函数题
![](http://img.wesiedu.com/upload/d/aa/daa97d85c41b7d27f05edaaedc1f0e45.jpg)
高等数学题.跪求第一大题所有小题的过程.悬赏酌情考虑.
![](http://img.wesiedu.com/upload/d/aa/daa97d85c41b7d27f05edaaedc1f0e45.jpg)
高等数学题.跪求第一大题所有小题的过程.悬赏酌情考虑.
每道题都是对等式两边的x求导
(1)2x-2yy'+2y+2xy'=2
(x-y)y'=1-x-y
y'=(1-x-y)/(x-y)
(2)y'=1+y'/y
yy'=y+y'
y'=y/(y-1)
(3)e^(x+y)*(1+y')=y+xy'
[e^(x+y)-x]y'=y-e^(x+y)
y'=[y-e^(x+y)]/[e^(x+y)-x]
(4)[(xy'-y)/x^2]/(1+y^2/x^2)=[(2x+2yy')/2√(x^2+y^2)]/√(x^2+y^2)
(xy'-y)/(x^2+y^2)=(x+yy')/(x^2+y^2)
xy'-y=x+yy'
y'=(x+y)/(x-y)
(5)e^(xy)*(y+xy')+y'lnx+y/x=-2sin2x
[e^(xy)*x+lnx]y'=-2sin2x-e^(xy)*y-y/x
y'=-[2sin2x+e^(xy)*y+y/x]/[e^(xy)*x+lnx]
(6)e^y+e^y*y'x+2yy'=0
(e^y*x+2y)y'=-e^y
y'=-(e^y)/(e^y*x+2y)
(7)1-cos(y/x)*(y'x-y)/x^2=0
y'x-y=x^2/cos(y/x)
y'=x*sec(y/x)+y/x
(8)-sin(x^2-y)*(2x-y')=1
y'-2x=csc(x^2-y)
y'=2x+csc(x^2-y)
再问: 我记得第一题的答案好像是分数。。
再答: 客气
(1)2x-2yy'+2y+2xy'=2
(x-y)y'=1-x-y
y'=(1-x-y)/(x-y)
(2)y'=1+y'/y
yy'=y+y'
y'=y/(y-1)
(3)e^(x+y)*(1+y')=y+xy'
[e^(x+y)-x]y'=y-e^(x+y)
y'=[y-e^(x+y)]/[e^(x+y)-x]
(4)[(xy'-y)/x^2]/(1+y^2/x^2)=[(2x+2yy')/2√(x^2+y^2)]/√(x^2+y^2)
(xy'-y)/(x^2+y^2)=(x+yy')/(x^2+y^2)
xy'-y=x+yy'
y'=(x+y)/(x-y)
(5)e^(xy)*(y+xy')+y'lnx+y/x=-2sin2x
[e^(xy)*x+lnx]y'=-2sin2x-e^(xy)*y-y/x
y'=-[2sin2x+e^(xy)*y+y/x]/[e^(xy)*x+lnx]
(6)e^y+e^y*y'x+2yy'=0
(e^y*x+2y)y'=-e^y
y'=-(e^y)/(e^y*x+2y)
(7)1-cos(y/x)*(y'x-y)/x^2=0
y'x-y=x^2/cos(y/x)
y'=x*sec(y/x)+y/x
(8)-sin(x^2-y)*(2x-y')=1
y'-2x=csc(x^2-y)
y'=2x+csc(x^2-y)
再问: 我记得第一题的答案好像是分数。。
再答: 客气