高数求dy/dx的题目,具体题目看图

高数求dy/dx的题目,具体题目看图
高数求dy/dx的题目,具体题目看图

高数求dy/dx的题目,具体题目看图

等一会我上图,一会在采纳

1/2ln(x²＋y²)=arctany/x
两边同时对x求导，得
1/2 *1/(x²＋y²)*(2x+2y*y')=1/[1+(y/x)²]* (y'x-y)/x²
x+yy'=y'x-y
(x-y)y'=x+y
y'=(x+y)/(x-y)
所以
dy=(x+y)/(x-y)dx

ln√(x^2+y^2)=arctany/x
1/2ln(x^2+y^2)=arctany/x
ln(x^2+y^2)=2arctany/x 两边对x求导得
1/(x^2+y^2)*(2x+2yy')=2*1/(1+[y/x)^2]*(y'x-y)/x^2
(2x+2yy')/(x^2+y^2)=2(y'x-y)/x^2 /[1+(y/x)^2]
...

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ln√(x^2+y^2)=arctany/x
1/2ln(x^2+y^2)=arctany/x
ln(x^2+y^2)=2arctany/x 两边对x求导得
1/(x^2+y^2)*(2x+2yy')=2*1/(1+[y/x)^2]*(y'x-y)/x^2
(2x+2yy')/(x^2+y^2)=2(y'x-y)/x^2 /[1+(y/x)^2]
=2(y'x-y)/(x^2+y^2)
2x+2yy'=2(y'x-y)
x+yy'=y'x-y
yy'-xy'=-x-y
y'=(-x-y)/(y-x)
=(x+y)/(x-y)
即
dy=(x+y)dx/(x-y)

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