求下列函数的导函数(1)y=xtanx-2sinx(2)y=lnxx+1-2x

求下列函数的导函数(1)y=xtanx-2sinx(2)y=lnxx+1-2x.
2024-12-11 21:53:24
推荐回答(1个)
回答1:

(1)∵y=xtanx-

2
sinx
=
xsinx
cosx
?
2
sinx

∴y′=
(xsinx)′cosx?xsinx(cosx)′
cos2x
?
?2cosx
sin2x

=
(sinx+xcosx)cosx+xsinxcosx
cos2x
+
2cosx
sin2x

=
(x+1)sinxcosx+xcos2x
cos2x
+
2cosx
sin2x

(2)∵y=
lnx
x+1
-2x
y′=
1
x
?(x+1)?lnx
(x+1)2
?2xln2

=
x+1?xlnx
x(x+1)2
?2xln2