求下列函数的导数 (1)y=x4-5/x2; (2)y=xtanx; (3)y=(x+1)(x+2)(x+3) (4)y=lgx-2x.
问题描述:
求下列函数的导数
(1)y=x4-
;5 x2
(2)y=xtanx;
(3)y=(x+1)(x+2)(x+3)
(4)y=lgx-2x.
答
(1)∵y=x4-
,5 x2
∴y′=4x3+10x-3;
(2)∵y=xtanx=
,xsinx cosx
∴y′=
=(xsinx)′cosx−(cosx)′xsinx cos2x
; sinxcosx+x cos2x
(3)∵y=(x+1)(x+2)(x+3),
∴y=(x2+3x+2)(x+3),
∴y′=3x2+12x+11.
(4)∵y=lgx-2x,
∴y′=
−2xln2.1 xln10