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

(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′=
1
xln10
2xln2