Question

求该函数的微分dy格式清晰.

Answer 1

arctanx/y=1/2ln(x²+y²)

两边同时对x求导,得

1/[1+(x/y)²]*(y-xy')/y²=1/2*1/(x²+y²)*(2x+2yy')

(y-xy')/(x²+y²)=(x+yy')/(x²+y²)

y-xy'=x+yy'

(x+y)y'=y-x

y'=(y-x)/(x+y)

所以

dy=[(y-x)/(x+y)]*dx