ln√(x눀+y눀)=arctany⼀x.求dy⼀dx

2025-01-19 03:08:17
推荐回答(2个)
回答1:

dln√(x²+y²)=darctan(y/x)
d(x²+y²)/[2(x²+y²)]=d(y/x)/[1+(y/x)²]
(xdx+ydy)/(x²+y²)=[(xdy-ydx)/x²]/[1+(y/x)²]
xdx+ydy=xdy-ydx
dy/dx=(x+y)/(x-y)

回答2:

令F(x, y)=ln√(x²+y²)-arctan(y/x)

Fx=2x. 1/(x²+y²)+y/x²·
1/(1+x²/y²)=(2x+y)/(x²+y²)

Fy=2y. 1/(x²+y²)-1/x·
1/(1+x²/y²)=(2y-x)/(x²+y²)

dy/dx=-Fx/Fy=2x+y)/(x-2y)